[1][2] His parents met while Benji attended Northwest Missouri State University, where he played Division II basketball after spending time at Northeastern Oklahoma A&M College.

[4] At the age of nine, Burke's father made him do everything with his left hand, including brushing his teeth and eating dinner, in order to develop his ambidexterity.

[4] Burke gave a verbal commitment to Penn State in 2009 after receiving his first Big Ten Conference offer, but later changed his mind to Michigan.

[1] As a sophomore, Burke made 5 of 6 free throws in overtime to help his team defeat Dublin Scioto High School by a 54–53 margin in a 2009 OHSAA Division I regional final.

[6] In the state championship game, he made one of two free throws to give Northland a 58–56 lead with 27.6 seconds left in what became a 60–58 win over Princeton High School.

[20] Burke was a 2009 OHSAA Division I State Champion, a Parade All-American (2011, second team)[21] and 2011 Associated Press Ohio Mr.

[22][23][24] Most elite level high school basketball players participate in the summer Amateur Athletic Union circuit as a complement to scholastic competition.

[20] Sources: The 2010–11 Michigan Wolverines team lost 2010–11 Big Ten Conference men's basketball season assist leader, point guard Darius Morris, to the Los Angeles Lakers in the 2011 NBA draft.

[50] On March 5 he earned his third consecutive and seventh overall Freshman of the Week honor when he averaged 20 points, 3 rebounds and 3 assists in road wins against Illinois and Penn State that clinched a share of the 2011–12 Big Ten Conference regular season championship.

[55] His three consecutive Big Ten Player of the Week awards to conclude the season coincided with the team winning 6 of its final 7 regular-season games.

[56][57] On January 4, Burke was named as one of the twenty Cousy Award Finalists along with fellow Big Ten point guards Aaron Craft and Jordan Taylor.

[73] As Burke weighed his decision, he became involved in a controversy when the Michigan State Spartans athletic director Mark Hollis communicated with him directly via Twitter.

[93][94][95] On November 27, Burke posted a career-high 11 assists, no turnovers and his first career double-double with 18 points in a 79–72 victory against number 18 NC State in the ACC–Big Ten Challenge.

[100][101] In the subsequent game on January 3, he posted a game-high 23 points and a career-high 4 steals in a 94–66 victory in the 2012–13 Big Ten Conference men's basketball season opener against Northwestern.

[119] On March 3, in the Ann Arbor version of the Michigan–Michigan State rivalry game, Burke had a career-high five steals, including 2 in the final 30 seconds of play, to go along with 21 points and 8 assists to key a 58–57 victory.

2 ranked Indiana with a share of the Big Ten regular season title at stake, Burke missed a last second shot at the rim, that was contested by Cody Zeller.

[127] On March 23, in the team's second game of the 2013 Tournament, in a 78–53 victory against VCU Burke tallied 7 assists, giving him a single-season total of 236 and surpassing Darius Morris as the school's single season record holder.

[131] It marked the first time that a player had 20 or more points and 10 or more assists in a Sweet Sixteen game since Billy Donovan did so in the 1986 tournament for Rick Pitino's Providence Friars.

"[140] Burke scored 24 points in the April 8, championship game against Louisville and made the 7-man All-Tournament team (which was revised multiple times) along with teammates McGary and Albrecht.

[170] On April 9 before boarding the airplane to return from the NCAA Final Four, head coach Beilein met with Burke, Hardaway, Robinson and McGary to direct them to seek the advice of the NBA advisory committee.

[182][183] On March 12, the U.S. Basketball Writers Association named Burke as District V Player of the Year on its 2012–13 Men's All-District V (OH, IN, IL, MI, MN, WI) Team, based upon voting from its national membership.

[191] On April 1, Burke was named first team All-American by the Associated Press, tying with Otto Porter for the most first-place votes and most total points.

[194] On April 4, Burke won the Bob Cousy Award and was named Associated Press College Basketball Player of the Year.

[220] With career highs of 21 points and 6 assists, Burke helped the Jazz record their first back-to-back wins of the season on December 2 against the Houston Rockets.

[256] On December 30, 2016, he scored a season-high 27 points off the bench as the Wizards beat the Brooklyn Nets 118–95 to win their third consecutive game and reach .500 for the first time in 2016–17.

[261] During the 2017 offseason, Burke agreed to a non-guaranteed deal with the Oklahoma City Thunder, but then changed his mind, opting to remain a free agent.

[285] Burke finished the season with averages of 12.6 points, 4.6 assists and 1.9 rebounds in 35 NBA games and he was recognized as a 2017–18 All-NBA G League Third Team honoree.

[288] On January 31, 2019, Burke was traded to the Dallas Mavericks along with Kristaps Porziņģis, Tim Hardaway Jr. and Courtney Lee in exchange for Dennis Smith Jr., DeAndre Jordan, Wesley Matthews and two future first round draft picks.

[295][296] On June 24, 2022, Burke, Boban Marjanović, Marquese Chriss, Sterling Brown and the draft rights to Wendell Moore Jr. were traded to the Houston Rockets in exchange for Christian Wood.

[297] On September 30, 2022, Burke was traded, along with David Nwaba, Sterling Brown, and Marquese Chriss, to the Oklahoma City Thunder in exchange for Derrick Favors, Ty Jerome, Maurice Harkless, Théo Maledon and a future second-round pick.