[7] He trained for several years at Nick Galis Hall, located near the center of Thessaloniki, Greece.

[9] Vezenkov began his pro career with the senior men's team of Aris, in the Greek League, in 2011, appearing in 10 games, with an average of 2.5 minutes on the floor.

[18] Vezenkov had originally planned to enter the 2015 NBA draft, but later withdrew his name from it before the deadline that was set for international players in June.

On 31 July 2015, Vezenkov signed a four-year deal (with the 4th year being optional) worth €2 million net income,[19] with the Spanish ACB League club FC Barcelona.

[21] Vezenkov's contract with FC Barcelona also included a buyout option for the NBA, set at the amount of €1 million.

[26] He recorded his EuroLeague career-high on 18 March 2021, scoring 31 points in an 80–84 win at Alba Berlin.

On 20 February 2022, he recorded 18 points and 13 rebounds in the Greek Cup Final against arch-rivals Panathinaikos, helping the club win its first title after 6 years.

On 27 April 2022, he scored 17 points and grabbed 9 rebounds in the 83–87 road win, in Game 3 of the playoff series against Monaco, helping his team regain homecourt advantage and eventually qualify for the EuroLeague Final Four, for the first time since 2017.

He finished the EuroLeague season averaging 13.7 points, 5.9 rebounds and a Performance Index Rating of 17.8.

On 17 June 2022, in Game 3 of the Greek League Finals against Panathinaikos, he recorded 25 points, 6 rebounds and 3 assists, with Olympiacos completing the domestic Double, having swept their rivals.

In 40 EuroLeague games, he averaged 17.6 points (66% from the field, 38% from beyond the arc, 88% from the free throw line), 6.8 rebounds, 1.9 assists, with a 21.5 PIR (Performance Index Rating), playing around 29 minutes per contest.

[30] On 14 January 2021, the Cleveland Cavaliers acquired his draft rights from the Nets in a multi-team trade involving James Harden.

[37] On January 10, 2025, he recorded his career high performance, scoring 45 points against Bayern Munich.

On February 6, 2025, he named Most Valuable Player of Round 25 of the 2024-2025 Turkish Airlines Euroleague Regular Season.

[57] Vezenkova decided to represent Cyprus, rather than Bulgaria, and she eventually became the captain of the Cypriot women's national basketball team.