Born in Germany, to two American parents who served in the US military there, Randolph's family eventually relocated to the United States, where he grew up in Pasadena, California.

The family later moved to Dallas, Texas, where Randolph soon became a standout at Woodrow Wilson High School, eventually being recruited by the Louisiana State Tigers.

After one year, Randolph left college, and entered the 2008 NBA draft, where he was chosen as the fourteenth pick overall by the Golden State Warriors.

[3] Washington called the team very talented, and referred to Randolph as the best player on the roster, but stated that, "as time went by, jealousy and agendas set in and took over.

[2] Although Randolph was named to the first team All-Area The Dallas Morning News boys basketball team, played in the Reebok Round Ball Classic, in Chicago, and the Adidas Derby Festival Classic in Kentucky (leading all scorers in both games), he was not chosen to play in the McDonald's All-American Game his senior year.

[5] Randolph was the only LSU Tiger to start all thirty-one games in his freshman season, and averaged 15.6 points, 8.5 rebounds, 1.2 assists, 1.13 steals, and 2.26 blocks per contest.

[5] Knowing there was a good chance he would be chosen in the first round, Randolph declared himself eligible for the 2008 NBA draft at the end of his freshman year at LSU.

[6] Some projected Randolph to go high in the year's draft because of his versatility and potential, while his detractors thought he might drop because of his thin frame and raw overall game.

[10] Early in his rookie season, Randolph received minimal playing time, causing some to question his attitude and work ethic, or if a possible rift might be developing between him and head coach Don Nelson.

[12] Nonetheless, the Warriors did play a fairly strong second half of the season, including Randolph, who averaged 13.5 points, 10.5 rebounds, 1.6 blocks, and 1.4 steals over the last twelve games of the year.

[12] After attending a Dallas Mavericks-San Antonio Spurs playoff game during the Warriors' offseason, Randolph became motivated to improve his play, hitting the gym hard to prepare for the following season.

[20] On February 22, 2011, Randolph was traded to the Minnesota Timberwolves in a three-way blockbuster deal which also involved the Denver Nuggets that brought Carmelo Anthony to New York.

[22] On June 26, 2014, Randolph was traded, along with Doug McDermott, to the Chicago Bulls for Gary Harris, Jusuf Nurkić and a 2015 second-round pick.