During the 2007–08 season at Kansas, Aldrich's freshman season, his playing time was limited due to playing behind future NBA draft picks Darrell Arthur, Sasha Kaun, and Darnell Jackson. He averaged three rebounds and 2.8 points a game on 8.3 minutes a game during the regular season. Statistically, Aldrich's best performance was an 11-point, 11-rebound outing in a win over Texas Tech on March 3, 2008. Probably the most crucial game for Aldrich was during the Final Four game between Kansas and North Carolina on April 5, 2008, when he played only 16 minutes but managed to grab 8 rebounds and score 7 points along with blocking 4 shots while also playing effective defense against National Player of the YearTyler Hansbrough, helping lead Kansas into the NCAA national championship game. They then defeated the Memphis Tigers to win their first Championship since 1988.
Sophomore season
With the departure of the other Jayhawk big men to the NBA draft, Aldrich became the premier big-man going into his sophomore season. Through the first 29 games, he averaged a double-double with 15.1 points and 10.8 rebounds in 29.7 minutes of play. He grabbed a career-high 20 rebounds in an 87–78 win over Oklahoma on February 23, 2009,. On March 8, 2009, Aldrich was named to the 2008–09 Big 12 All-conference first team. On March 22, 2009 Aldrich recorded the first official triple-double in the history of Kansas basketball against Dayton in the second round of the NCAA tournament. Aldrich accumulated 13 points, 20 rebounds, and 10 blocks in a 60–43 victory, which was the second triple double in NCAA history to include blocks, former LSU center Shaquille O'Neal recorded the other. On Monday, April 13, Aldrich announced that he would return to KU for his Junior season.
On March 29, 2010, Aldrich announced that he would forgo his final season of collegiate eligibility and enter the 2010 NBA draft. He was the 11th pick, selected by the New Orleans Hornets, who traded his rights on draft day to the Oklahoma City Thunder. On August 6, 2010, Aldrich signed a two-year contract with the Thunder with a two-year option. On November 24, 2010, the Thunder assigned Aldrich to the Tulsa 66ers of the NBA D-League. He was recalled on December 6, 2010, but sent back to Tulsa on December 30, 2010. He was again recalled on February 2, 2011, and assigned for a third time on March 30, 2011. Aldrich reached the 2012 NBA Finals with the Thunder, but the team lost to the Miami Heat.
On September 24, 2013, Aldrich signed with the New York Knicks. On January 29, 2014, he was assigned to the Erie BayHawks. He was recalled the next day. He went on to record his first double-double in his first NBA start on March 12, 2014. On July 11, 2014, Aldrich re-signed with the Knicks. On April 11, 2015, he scored a career-high 19 points in an 80-79 win over the Orlando Magic.
Los Angeles Clippers (2015–2016)
On July 13, 2015, Aldrich signed with the Los Angeles Clippers. On January 13, 2016, with starting center DeAndre Jordan out, Aldrich had a then season-best game with 19 points and 7 rebounds in a 104–90 win over the Miami Heat. On April 8, 2016, he recorded 21 points and 18 rebounds and a career-high five steals in a 102–99 overtime win over the Utah Jazz.
Minnesota Timberwolves (2016–2018)
On July 13, 2016, Aldrich signed a three-year, $22 million deal with the Minnesota Timberwolves. On June 30, 2018, Aldrich was waived by the Timberwolves. On September 18, 2018, Aldrich signed with the Atlanta Hawks but was waived by the Hawks on October 2, 2018 as their first training camp cut.
Tianjin Golden Lions (2018)
On October 10, 2018, Aldrich signed with the Tianjin Golden Lions of the Chinese Basketball Association.
