The San Francisco Giants of Major League Baseball originated in New York City as the New York Gothams in 1883 and were known as the New York Giants from 1885 until the team relocated to San Francisco after the 1957 season. During most of their 75 seasons in New York City, the Giants played home games at various incarnations of the Polo Grounds in Upper Manhattan.

Numerous inductees of the National Baseball Hall of Fame and Museum in Cooperstown, New York played for the New York Giants, including John McGraw, Mel Ott, Bill Terry, Willie Mays, Monte Irvin, and Travis Jackson. During the club's tenure in New York, it won five of the franchise's eight World Series wins and 17 of its 23 National League pennants. Famous moments in the Giants' New York history include the 1922 World Series, in which the Giants swept the Yankees in four games, Bobby Thomson's 1951 home run known as the "Shot Heard 'Round the World", and the defensive feat by Willie Mays during the first game of the 1954 World Series known as "the Catch".

The Giants had intense rivalries with their fellow New York teams the New York Yankees and the Brooklyn Dodgers, facing the Yankees in six World Series and playing the league rival Dodgers multiple times per season. Games between any two of these three teams were known collectively as the Subway Series. The Dodgers-Giants rivalry continues, as both teams moved to the West Coast in California after the 1957 season, with the Dodgers relocating to Los Angeles. The New York Giants of the National Football League are named after the team.

The Giants began as the second baseball club founded by millionaire tobacconist John B. Day and veteran amateur baseball player Jim Mutrie. The Gothams, as the Giants were originally known, entered the National League seven years after its 1876 formation, in 1883, while their other club, the Metropolitans played in the rival American Association (1882-1891). Nearly half of the original Gothams players were members of the disbanded Troy Trojans in upstate New York, whose place in the National League the Gothams inherited. While the Metropolitans were initially the more successful club, after they won the 1884 AA championship, Day and Mutrie began moving star players to the NL Gothams, whose fortunes improved while the Metropolitans' afterwards slumped.

It is said that after one particularly satisfying victory over the Philadelphia Phillies, Mutrie (who was also the team's manager) stormed into the dressing room and exclaimed, "My big fellows! My giants!"^[1] From then on (1885), the club was known as the Giants. However, more recent research has suggested that the New York World was already widely using the Giants nickname throughout the 1885 season, before the legendary game was played.^[2]

The team won its first National League pennant in 1888, as well as a victory over the St. Louis Browns in an early incarnation of the pre-modern-era World Series. They repeated as champions the next year with a pennant and world championship victory over the Brooklyn Bridegrooms.

The Giants' original home stadium, the Polo Grounds, also dates from this early era. It was originally located north of Central Park adjacent to Fifth and Sixth Avenues and 110th and 112th Streets, in Harlem in upper Manhattan. After their eviction from that first incarnation of the Polo Grounds after the 1888 season, they moved further uptown to various fields which they also named the "Polo Grounds" located between 155th and 159th Streets in Harlem and Washington Heights, playing in the Washington Heights located famous Polo Grounds until the end of the 1957 season, when they moved to San Francisco.

The Giants were a powerhouse in the late 1880s, winning their first two National League Pennants and World Championships in 1888 & 1889. But nearly all of the Giants' stars jumped to the upstart newly-organized rival loop, the Players' League, whose New York franchise was also named the Giants, in 1890. The new team even built a stadium next door to the NL Polo Grounds. With a decimated roster, the NL Giants finished a distant sixth. Attendance took a nosedive, and the financial strain affected Day's tobacco business as well. The Players' League dissolved after the single season, and Day sold a minority interest in his NL Giants to the defunct PL Giants' principal backer, Edward Talcott. As a condition of the sale, Day had to fire Mutrie as manager. Although the Giants rebounded to third place in 1891, Day was forced to sell a controlling interest to Talcott at the end of the '91 season.

Four years later, Talcott sold the Giants to Andrew Freedman, a real estate developer with ties to the Tammany Hall political machine/of the city/state Democratic Party running New York City. Freedman was one of the most detested owners in baseball history, getting into heated disputes with other owners, writers and his own players, most famously with star pitcher Amos Rusie, author of the first Giants no-hitter. When Freedman offered Rusie only $2,500 for 1896, the disgruntled hurler sat out the entire season. Attendance fell off throughout the league without Rusie, prompting the other owners to chip in $50,000 to get him to return for 1897. Freedman even hired former owner Day as manager for part of the 1899 season.

In 1902, after a series of disastrous moves that left the Giants 53½ games behind the front-runner, Freedman signed John McGraw as player-manager, convincing him to jump in mid-season from the Baltimore Orioles (1901-1902) of the fledgling American League and bring with him several of his teammates. McGraw went on to manage the Giants for three decades until 1932, one of the longest and most successful tenures in professional sports. Hiring "Mr. McGraw," as his players referred to him, was one of Freedman's last significant moves as owner of the Giants, since after that 1902 season he was forced to sell his interest in the club to John T. Brush. McGraw went on to manage the Giants to nine National League pennants (in 1904-1905, 1911–1913, 1914) and three World Series championships (in 1905 & 1921-1922), with a tenth pennant and fourth world championship as Giants owner in 1933 under his handpicked player-manager successor, Bill Terry.

The Giants already had their share of stars beginning in the 1880s & 1890s, such as "Smiling" Mickey Welch, Roger Connor, Tim Keefe, Jim O'Rourke and John Montgomery Ward, the player-lawyer who formed the renegade Players' League in 1890 to protest unfair player contracts. McGraw, a veteran of the infamous 1890s Baltimore Orioles, in his three decades managing the Giants, cultivated a new crop of baseball heroes with names like Christy Mathewson, "Iron Man" Joe McGinnity, Jim Thorpe, Red Ames, Casey Stengel, Art Nehf, Edd Roush, Rogers Hornsby, Bill Terry and Mel Ott.

The Giants under McGraw famously snubbed their first modern World Series chance in 1904, established as the price of peace with the rival Americans, first played the year before, by refusing the invitation to play the reigning world champion Boston Americans (now known as the Boston Red Sox) because McGraw considered the newly established American League of 1901, as little more than a minor league and disliked its firebrand president, Ban Johnson. He also resented his Giants' new intra-city rival New York Highlanders, (from the old relocated charter AL franchise Baltimore Orioles), who almost won the pennant but lost to Boston on the last day, and stuck by his refusal to play whoever won the 1904 AL pennant. Of note, McGraw had managed the relocated Highlanders franchise in their first two seasons (1901–1902), when they were playing in Baltimore.

The ensuing criticism resulted in Brush's taking the lead to formalize the rules and format of the World Series. The Giants won the 1905 World Series over Connie Mack's Philadelphia Athletics, with Christy Mathewson nearly winning the series single-handedly with a still-standing record three complete-game shutouts and 27 consecutive scoreless innings in that one World Series.

The Giants then had several frustrating years. In 1908, they finished in a tie with the Chicago Cubs due to a late-season home tie game with the Cubs resulting from the Fred Merkle baserunning "boner". They lost the postseason replay of the tie game (ordered by NL president Harry Pulliam) to the Cubs (after disgruntled Giants fans had set fire to the stands the morning of the game), who would go on to win their second (consecutive, and their last for the next 108 years!!) World Series. That post-season game was further darkened by a story that someone on the Giants had attempted to bribe umpire Bill Klem. This could have been a disastrous scandal for baseball, but because Klem was honest and the Giants lost the duel between Christy Mathewson and Mordecai "Three-Fingered" Brown 4–2, it faded over time.

The Giants experienced a mixture of success and hard luck in the early 1910s, losing three straight World Series in 1911–1913 to the A's, Red Sox and A's again (two seasons later, both the Giants and the A's, decimated by the short-lived rival third loop, the Federal League of 1914-1915, with the "jumping ship" signings of many of their stars, finished in eighth [last] place). After losing the 1917 Series to the Chicago White Sox (the last "Chisox Series" win until 2005), the Giants played in four straight World Series in the early 1920s, winning the first two over their Polo Grounds fellow tenants, the Yankees (after winning the first two of their many pennants, led by their new young slugger and former Red Sox and Orioles pitcher George Herman "Babe" Ruth), then losing to the Yankees in 1923 after old Yankee Stadium had opened that May. They also lost in 1924, when the Washington Senators won their only World Series while in D.C.

McGraw handed over the team to Bill Terry after the 1932 season, and Terry played for and managed the Giants for ten years, winning three pennants, defeating the Senators in the 1933 World Series but swept by the Yankees in consecutive fall classics, 1936 and 1937. Aside from Terry himself, the other stars of the era were slugger Mel Ott and southpaw hurler Carl Hubbell. Known as "King Carl" and "The Meal Ticket", Hubbell gained fame in the first two innings of the 1934 All-Star Game (played at the Polo Grounds) by striking out five future AL Hall of Famers in a row: Babe Ruth, Lou Gehrig, Jimmie Foxx, Al Simmons and Joe Cronin.

Ott succeeded Terry as manager in 1942, but the war years proved to be difficult for the Giants. Midway during the 1948 season Brooklyn Dodgers Leo Durocher left as Dodgers skipper to manage the Giants, not without controversy. Not only was such a midseason managerial switch unprecedented, but Durocher had been accused of gambling in 1947 and subsequently suspended for that whole season by Baseball Commissioner Albert "Happy" Chandler. Durocher's ensuing eight full seasons managing the Giants proved some of the most memorable for their fans, particularly because of the arrival of five-tool superstar Willie Mays, their two pennants in 1951 & 1954, their unexpected sweep of the powerful (111-43) Cleveland Indians in the 1954 World Series and arguably the two most famous plays in Giants history.

The "Shot Heard 'Round the World," or Bobby Thomson's come-from-behind ninth-inning walk-off home run that won the National League pennant for the Giants over their bitter rivals, the Brooklyn Dodgers, in the deciding game of a three-game playoff series ended one of baseball's most memorable pennant races. The Giants had been 13 1/2 games behind the league-leading Dodgers in August, but under Durocher's guidance and with a 16-game winning streak, got hot and caught the Dodgers to tie for the lead on the next-to-last day of the season.

In Game 1 of the 1954 World Series at the Polo Grounds against the Cleveland Indians, Willie Mays made "The Catch," a dramatic over-the-shoulder catch of a fly ball by Vic Wertz after sprinting with his back to the plate on a dead run to deepest center field. At the time the game was tied 2–2 in the eighth inning, with men on first and second and nobody out. Mays caught the ball 450 ft (140 m) from the plate, whirled and threw the ball to the infield, keeping the lead runner, Larry Doby, from scoring. Although Doby took third after the catch, he was stranded there and the Giants won on Dusty Rhodes' tenth-inning pinch-hit walk-off home run with two aboard, 5-2.

The underdog Giants went on to sweep the series in four straight, despite the Indians' American League 111-43 regular season. The 1954 World Series title would be their last appearance in the World Series as the New York Giants, with the team moving to San Francisco to start the 1958 season.

In addition to Bobby Thomson and Willie Mays, other memorable New York Giants of the 1950s include Hall of Fame manager Leo Durocher, coach Herman Franks, Hall of Fame outfielder Monte Irvin, outfielder and runner-up for the 1954 NL batting championship (won by Willie Mays) Don Mueller, Hall of Fame knuckleball relief pitcher Hoyt Wilhelm, starting pitchers Larry Jansen, Sal Maglie, Jim Hearn, Marv Grissom, Dave Koslo, Don Liddle, Max Lanier, Rubén Gómez, Al Worthington, and Johnny Antonelli, catcher Wes Westrum, catchers Ray Katt and Sal Yvars, shortstop Alvin Dark, third baseman Hank Thompson, first baseman Whitey Lockman, second basemen Davey Williams and Eddie Stanky, outfielder-pitcher Clint Hartung and utility men Johnny Mize, Bill Rigney, Daryl Spencer, Bobby Hofman, Joey Amalfitano, Tookie Gilbert, and 1954 Series hero Dusty Rhodes, among others. In the late 1950s and after the move to San Francisco two Hall of Fame first basemen, Orlando Cepeda and Willie McCovey, joined the team.

The Giants' final three years in New York City were unmemorable. They stumbled to third place the year after their World Series win, and attendance fell off precipitously. While seeking a new stadium to replace the crumbling Polo Grounds, the Giants began to contemplate a move from New York, initially considering Metropolitan Stadium in Bloomington, Minnesota, which was home to their top farm team, the Minneapolis Millers. Under the rules of the time, the Giants' ownership of the Millers gave them priority rights to a major league team in the area (the Washington Senators wound up there as the Minnesota Twins in 1961).

At this time, the Giants were approached by San Francisco mayor George Christopher. Despite objections from shareholders such as Joan Whitney Payson, majority owner Horace Stoneham entered into negotiations with San Francisco officials around the same time the Dodgers' owner Walter O'Malley was courting the city of Los Angeles. O'Malley had been told that the Dodgers would not be allowed to move to Los Angeles unless a second team moved to California as well. He pushed Stoneham toward relocation, and so in the summer of 1957 both the Giants and Brooklyn Dodgers announced their moves to California, ending the three-team golden age of baseball in New York City.

New York would remain a one-team town with the New York Yankees until 1962, when Joan Payson founded the New York Mets and brought National League baseball back to the city (as part of MLB's first wave of expansion). Owners Payson and M. Donald Grant, who became the Mets' chairman, had been the only Giants board members to vote against the Giants' move to California. The "NY" script on the Giants' caps and the orange trim on their uniforms, along with the blue background used by the Dodgers, would be adopted by the Mets, honoring their New York NL forebears with a blend of Giants orange and Dodgers blue.