He transferred to Michigan after leading Williams College to the 2014 NCAA Division III men's basketball tournament championship game.

Robinson has set numerous three-point shot records during his tenure with the Heat and has helped Miami reach the NBA Finals in 2020 and 2023.

[1] Robinson grew up in the town of New Castle, New Hampshire (population 1,000), where his Maude H. Trefethen Elementary School 6th grade graduating class was composed of just four students.

[3] Following his senior season, Robinson played on the spring and summer Amateur Athletic Union (AAU) circuit and did a postgraduate year at Phillips Exeter Academy in order to increase his college prospects.

Robinson posted 24 points and 10 rebounds in the championship game, earning the Tournament MVP in addition to 2013 New England Preparatory School Athletic Council (NEPSAC) Class A All-League first team honors.

[2][3][11] At the time, Williams was ranked the number one liberal arts college in the country according to U.S. News & World Report,[3] and the school was a Division III basketball powerhouse.

[3] In 2013, Robinson led Phillips Exeter Academy to its first NEPSAC Class A championship victory on March 10 against Choate Rosemary Hall with a 24-point, 10-rebound MVP performance.

[3][13] Prior to the November 15, 2013, season opener against Southern Vermont College, Williams was ranked third among Division III teams according to the preseason poll.

[14] Williams reached the 2014 NCAA Men's Division III basketball tournament championship game, but fell 75–73 to University of Wisconsin–Whitewater as Robinson scored 17 points.

[15] After Williams took a one-point lead with 4.9 seconds left, Wisconsin pushed the ball upcourt without calling time-out to score the winning basket in what Chris Strauss of USA Today described as the best NCAA basketball tournament game of the weekend.

Robinson had posted 30 points in the tournament semifinals against bitter rival Amherst College who had defeated Williams in the season's three previous meetings.

[8] After his freshman success, he had decided that he would only leave Williams to play for a winning program that was an elite academic institution and that used a system and style that he had become used to.

[4][24] In Robinson's second game for the 2015–16 Michigan Wolverines, he posted 19 points on 6–6 shooting (5–5 three-point shots) from the floor against Elon on November 16, 2015.

[34][35] On January 12, with leading scorer Caris LeVert sidelined, Michigan defeated Maryland[36] 70–67 as Robinson contributed 17 points on 5–9 three-point shooting.

[51][52][53] The following day, in the quarterfinals against first-seeded Indiana, Robinson again put Michigan in position to win by tying the score with a three-point shot with 46 seconds remaining (this time in regulation).

[56][57] On March 16, in the First Four round of the 2016 NCAA Division I men's basketball tournament, Michigan defeated Tulsa, 67–62, with support from Robinson who recorded his first double-double as a Wolverine with 13 points and a season-high 11 rebounds.

[58][59] Robinson finished the season second to Bryn Forbes (48.1%) among Big Ten players in three-point field goal percentage with a 45.0% mark.

[67] Late in the season, he began producing The Dak and Dunc Show podcast with teammate Andrew Dakich for WCBN-FM Sports, which was available on iTunes.

[83][84] On March 1 in the 2018 Big Ten Conference men's basketball tournament Robinson helped lead Michigan to a 77–71 overtime victory over Iowa after his co-captains, Wagner and Abdur-Rahkman, fouled out by converting a go-ahead three-point shot with 2:17 remaining in overtime and two free throws to give Michigan a two-possession lead with 10 seconds remaining.

[85][86][87] The following day in the quarterfinals of the Big Ten tournament Robinson scored his 1,000th career point on his second three-point field goal of the first half.

[99] Over the course of three seasons, Robinson finished his career with 237 made three-point shots (on 41.9% shooting),[97] placing fourth on Michigan's all-time list.

[101] After 5 Summer League games in which he averaged 12.4 points and 2.4 rebounds while shooting 58% (22-for-38)[97] from the field including 63% (17-for-27) on three-point shots, he agreed to a two-way contract with the Miami Heat and Sioux Falls Skyforce on July 10, 2018.

[111] Robinson made his NBA debut in the Heat's fourth game of the season on October 24, against the New York Knicks with three points and four rebounds in 10 minutes of action.

[112][113] He scored 15 points as a starter when Sioux Falls opened its season on November 2 with a 112–101 victory against the Fort Wayne Mad Ants.

[127] On November 20, Robinson posted a career-high 29 points against his college coach John Beilein's Cleveland Cavaliers, establishing Heat records with seven three-point shots in a quarter and eight in a half.

[133] Following his performance, The Wall Street Journal called Robinson "the most improbable player in the NBA" and "one of the best shooters on the planet" in an article on December 13, 2019.

[146] Robinson debuted in his first NBA playoff game on August 18, with 2-for-8 3-point shooting for six points, three rebounds and one assist against the Indiana Pacers.

On December 25, 2020, Robinson made seven three-point shots, which tied Brandon Ingram for the NBA Christmas Day record that was equaled hours later by Kyrie Irving.

[154] On January 6 against the Boston Celtics, Robinson surpassed Damian Lillard and Luka Dončić (117), by posting his 300th made three-point shot in his 95th career game.

[156] The Chicago Bulls snapped Robinson's franchise record 25-game streak of consecutive games with multiple three-point conversions on April 26.