The senate president often ranks high in a jurisdiction's succession for its top executive office: for example, the President of the Senate of Nigeria is second in line for succession to the presidency, after only the Vice President of the Federal Republic, while in France, which has no vice president, the Senate President is first in line to succeed to the Presidential powers and duties.
The Argentine Senate is presided over by the Vice-President of the Republic, currently Gabriela Michetti. This was a recent expansion of the Vice-President's powers introduced as part of the 1994 constitutional amendments ( Constitution, Art. 57). The Vice-President may only cast a vote to break a tied Senate vote.
The President of the Australian Senate is a senator, traditionally a member of the governing party or coalition, elected by the Senate at the beginning of each parliament as the first item of business. They are assisted by a Deputy President who is traditionally a member of the largest opposition party.  The current president is Stephen Parry, a Liberal senator from Tasmania, who has held the office since 7 July 2014. 
At the start of every parliamentary session, the Senate of Barbados elects a President and a Vice President, neither of whom may be ministers or parliamentary secretaries. Prior to the January 2008 general election, the positions were held by Sir Fred Gollop and Dame Patricia Symmonds.
The presiding officer of the Belgian Senate is elected by the senators at the beginning of each parliamentary term. The President of the Senate is customarily a member of a majority party with a great deal of political experience. The president presides over the plenary assembly of the Senate, guides and controls debates in the assembly, is responsible for ensuring the democratic functioning of the Senate, maintains order and security in the assembly and for enforcing the Rules of the Senate, and represents the Senate at both the national (to the other institutions) and the international level.
The President of the Senate, together with the President of the Chamber of Representatives, ranks immediately behind the King in the order of precedence. The elder of the two takes the second place in the order of precedence. The Presidents of the Senate and the Chamber rank above the Prime Minister.
The Senate of Belize elects both a president and a vice-president upon first convening after a general election. The person elected president may be a senator (provided he/she does not concurrently hold a ministerial position) or a person external to the Senate. The vice-president must be a member of the Senate who does not hold a ministerial portfolio. ( Constitution, section 66.) 
The current President is Andrea Gill, with Juliet Thimbriel as Vice-President.
The President of the Federal Senate is the third in order to succeed the president (only below the Vice President and the President of the Chamber of Deputies). It is also the president of the National Congress, which includes the Senate and the Chamber of Deputies.
The Senate of Cambodia is led by a 12-person permanent commission (bureau) , which is in turn chaired by the President of the Senate, currently Say Chhum. He is assisted by a First and a Second Vice-President.  The President and Vice-Presidents are elected as the first item of business at the start of every legislative session. 
While the Speaker of the Canadian Senate, who serves as the presiding officer of the Senate of Canada, is not described as a "president" in English, the position is called Président du Sénat in French. He is appointed by the Governor General on the advice of the Prime Minister.
The members of the former Senate of Fiji (abolished in 2012) used to elect from among their number both a President and Vice-President, whose roles were similar to those of the Speaker and Deputy Speaker of the House of Representatives, respectively.
In the Free City of Danzig (1920–1939/1945), the Senate (or Senat in German) was the executive branch, with Senators ( Senatoren ) being the holders of ministerial portfolios. In Danzig the President of the Senate ( Präsident des Senats ) was an office equivalent to that of prime minister in other countries.
The Senate of France elects a president from among its own number. The President of the French Senate stands first in line of succession in case of death or resignation of the President of the Republic, becoming acting president until a presidential election can be held. This most recently occurred with Alain Poher, who was senate president from 1968 to 1992 and who served as interim president on two occasions: following Charles de Gaulle's resignation in 1969, and following Georges Pompidou's death in office in 1974.
In the German states of Bremen ( Senate of Bremen) and Hamburg ( Senate of Hamburg), the Senates (or Senate in German) are the executive branch, with Senators ( Senatoren ) being the holders of ministerial portfolios. In these Länder, the President of the Senate ( Präsident des Senats ) is an office equivalent to that of minister-president in other German Länder.
The Senate of Italy holds its first sitting no later than 20 days after a general election. That session, presided by the oldest senator, proceeds to elect the President of the Senate for the following parliamentary period. On the first two attempts at voting, an absolute majority (a majority of all senators) is needed; if a third round is needed, a candidate can be elected by a majority of the senators present and voting. If this third round fails to produce a winner, a final ballot is held between the two senators with the highest votes in the previous ballot. In the case of a tie, the elder senator is deemed the winner.
In addition to overseeing the business of the chamber, chairing and regulating debates, deciding whether motions and bills are admissible, representing the Senate, etc., the President of the Senate stands in for the President of the Republic when s/he is unable to perform his/her duties. 
The Senate of Malaysia elects a president from its members, who is comparable to the Speaker of the House of Representatives. The position is partisan and has usually been held by a member of the Government party.
The Senate of Mexico, at the beginning of each annual legislative session, elects an Executive Board (Mesa Directiva) from among its 128 members. The Executive Board comprises a president, three vice-presidents, and four secretaries, elected by an absolute majority of the Senators. Members of the Executive Board may be re-elected for the following year without restriction. The President of the Executive Board also serves as the President of the Senate.
The first session of the Senate is headed by the eldest senator. In that session the senators elect the Standing Bureau of the Romanian Senate. It consists of the President of the Senate, four vice-presidents, four secretaries, and four quaestors. The President of the Standing Bureau also serves as the President of the Senate. The President is elected, by secret ballot, for the duration of the legislative period.  The Senate president succeeds temporarily the President of Romania if the latter resigns, is suspended, incapacitated or dies in office. (He/she continues to be President of the Senate during the ad-interim presidency of the country. He/she acts as President until a new president is elected).
- For a listing, see: Senate of South Africa#Presidents of the Senate of South Africa (1910-1980) and (1994-1997)
Trinidad and Tobago
The President of the Senate of Trinidad and Tobago, who is generally elected from the government benches, chairs debates in the chamber and stands in for the country's president during periods of absence or illness (Constitution, section 27).  A Vice-President of the Senate is also elected from among the senators. The current President of the Senate is Christine Kangaloo.
The Vice President of the United States is assigned the responsibility of presiding over the Senate and designated as its president by the United States Constitution. The vice president, as President of the Senate, has the authority ( ex officio , for he or she is not an elected member of the Senate) to cast a tie-breaking vote. Other than this, the rules of the Senate grant its president very little power (in contrast to the powerful office of Speaker of the House of Representatives).
While vice presidents used to regularly preside over the Senate, modern vice presidents have done so only rarely, usually only when swearing in new senators, during joint sessions, announcing the result of a vote on a significant bill or confirmation, or when casting a tie-breaking vote. The Senate chooses a president pro tempore to preside in the vice president's absence. Modern presidents pro tempore, too, rarely preside over the Senate. In practice, the junior senators of the majority party typically preside in order to learn Senate procedure.
Vice presidents have cast 261 tie-breaking votes since the U.S. federal government was established in 1789. The vice president with the most tie breaking votes is John Adams (served 1789–1797) with 29. The current Vice President Mike Pence, in office since January 2017, has made six tie-breaking votes. 
U.S. state senates
In state governments of the United States, the presiding officer of the state senate (the upper house) is a matter decided by the state's constitution. Some states designate the lieutenant governor as president of the senate, while in other states, the Senate elects its own president. The Tennessee Senate elects a senator Speaker of the Senate, who is given the title of Lieutenant Governor.
Similarly, New Hampshire has no lieutenant governor, but the state senate elects a president who is the de facto lieutenant governor, given that in the event of the governor's death, resignation, or inability to serve, the president of the senate acts as governor until the vacancy is filled. New Jersey previously used the same system, but with the important proviso that the Senate president continued to serve in that position while also serving as acting governor. After Christine Todd Whitman resigned as governor, Donald DiFrancesco spent nearly a year as acting governor. As a result of his tenure, questions were raised about the propriety of such a system, particularly with regard to separation of powers -related issues. A constitutional amendment was enacted in 2005 to create the office of lieutenant governor effective at the 2009 election.