High school career
He was ranked as the 9th overall linebacker prospect in the nation by Scout.com.  He also was ranked as the 55th best prospect in the state of Texas by Rivals.com.  He was selected to the Preseason All-Greater Team before his Senior season at High school.  He was selected to the All-Greater Houston team while at high school.  He also was named to the third team of Dave Campbell's Texas Football Magazine's Super Team. 
|Name||Hometown||High school / college||Height||Weight||40 ‡||Commit date|
| Damion Square |
|Houston, Texas||Yates High School||6 ft 3 in (1.91 m)||270 lb (120 kg)||4.78||Jan 11, 2008|
|Recruiting star ratings : Scout : Rivals : 247Sports : ESPN grade: 79|
|Overall recruiting rankings: Scout : 9 ( SLB ) Rivals : 37 ( DT ) 247Sports : 16 (SDE) ESPN : 24 (DE)|
He played college football at Alabama. In his sophomore season, he finished the season with 27 tackles and 3 sacks.  He finished his last two seasons with a total of 65 tackles, 4.5 sacks, and 2 pass deflections.  On July 19, 2012, He was selected to the preseason all-SEC second team prior to his Senior season. 
Kansas City Chiefs
Square was claimed off waivers by the Kansas City Chiefs on September 1, 2014. He was released by the Chiefs on October 31.
San Diego / Los Angeles Chargers
After he was released by the Chiefs, Square was claimed off waivers by the San Diego Chargers on November 3, 2014. On March 11, 2016, he was re-signed by the Chargers to a one-year contract. On September 3, 2016, he was suspended by the NFL for the first four games of the 2016 NFL season . 
On March 10, 2017, Square signed a two-year contract extension with the Chargers.