His agent Thies Bliemeister said Son was so determined to make himself a success in Europe that he learned German by watching episodes of SpongeBob SquarePants.

After participating in the FIFA U-17 World Cup, he formally joined Hamburger SV's youth academy in November 2009[32] He was impressive in the 2010–11 pre-season, leading the team with nine goals, and signed his first professional contract on his 18th birthday.

[44] Following Hamburger SV's 2012–13 offseason moves, which saw the transfers of the team's strikers Mladen Petrić and Paolo Guerrero to Fulham and Corinthians respectively, manager Thorsten Fink chose to name Son a starter.

[48] Son adjusted quickly to his new club in the pre-season, scoring three goals in his first three appearances for the team in exhibition matches (against 1860 Munich, Udinese and KAS Eupen respectively).

[71] In the same match, he was racially abused by a section of the Millwall fans who chanted "DVD" and "he's selling three for a fiver" whenever he touched the ball, referencing a stereotype towards east Asians.

[91] On 9 April 2019, Son scored the first European competition goal at the Tottenham Hotspur Stadium in a 1–0 win against Manchester City in the quarterfinals of the 2018–19 Champions League.

His brace also saw him become the highest scoring Asian player in the history of the tournament with 12 goals, overtaking the previous record holder, Maxim Shatskikh.

[96] On 3 November, Son was sent off during a 1–1 draw with Everton after sliding into André Gomes from behind, causing him to fall awkwardly and suffer a severe ankle injury.

[98] However, many professionals including former Everton player Kevin Kilbane expressed criticism of the red card decision, and Tottenham made an appeal to the Football Association against the dismissal.

[99][100] Three days after this incident, in a 4–0 Champions League away game to Red Star Belgrade, in which Son scored a brace, rather than celebrating his first goal, he apologised to the camera for what happened at Goodison Park.

[101][102] On 23 November 2019, Son scored Tottenham's first goal with José Mourinho as manager, earning him Man-of-the-match in a 3–2 Spurs victory against West Ham.

[111] Head coach José Mourinho declared at a later stage that he was not optimistic regarding Son's injury and that it was likely that the South Korean would be sidelined for the rest of the season.

[112] On 6 April 2020, while football was suspended due to the COVID-19 pandemic in Europe, it was confirmed that Son would carry out his mandatory military service for South Korea.

[117] On 28 January 2021, Son's counterpart on the Korean Women's National Team, Cho So-hyun joined FA WSL side Tottenham Hotspur on loan for the remainder of the 2020–21 season.

[125] On 4 November, he scored in new manager Antonio Conte's first match in charge, a 3–2 victory over Vitesse in the group stage of the Europa Conference League.

[133] On 1 November, Son collided with Marseille's Chancel Mbemba during the final matchday of the UEFA Champions League group stage, which caused an orbital fracture in his left eye.

[135] On 19 February 2023, after scoring a 72nd-minute goal against West Ham to secure a 2–0 victory, Son was subjected to online racist abuse, which was condemned as "utterly reprehensible" by Tottenham and the Kick It Out anti-racism organisation.

[136] Despite enduring a difficult season for Tottenham, on 8 April, Son scored his 100th Premier League goal in a 2–1 win over Brighton & Hove Albion, and became the first Asian player to reach that landmark.

Following the match, Son earned the praise of his manager Ange Postecoglou, stating that "he's been outstanding as a leader and as a player [...] we have put him in that nine position now and he just works so hard.

[144] On 10 February 2024, Son made his return from the 2023 AFC Asian Cup, assisting teammate Brennan Johnson to score a 90+6th-minute goal, a late minute winner in a 2–1 win over Brighton & Hove Albion.

Despite Son affirming his interest and the KFA's efforts, Bayer Leverkusen refused to release him, as his absence would mean the team would lose him for at least six matches.

[167] On 23 June, Son scored a goal from outside the penalty area – a curling strike into the top corner – though his side was defeated with a 2–1 loss to Mexico in their second group stage match of the World Cup.

[168] On 27 June, during their final group stage match, he scored the second goal in the 97th minute in their 2–0 victory over world champions Germany, sealing their elimination.

[172][173] In the gold medal match, Son assisted in both extra-time goals in a 2–1 victory over Japan, which guaranteed the entire squad's exemption from mandatory military service.

[174][175] Son was called up as captain for the 2019 AFC Asian Cup in the United Arab Emirates by Paulo Bento, but missed the first two group matches due to an agreement with Tottenham Hotspur related to his call-up.

[177] However, his play at the tournament was lethargic due to lack of physical strength in his busy schedule,[178] and he returned to London following his team's defeat in the quarter-finals to the eventual champion Qatar.

"[188][189] Son is known for his two-footed ability, explosive pace, positional sense, movement, close control and clinical finishing which make him especially effective on the counter-attack.

[199] In March 2023, Son was named as the global face of the Burberry's first campaign under its new chief creative officer Daniel Lee along with Georgia May Jagger.

[203] Son has two officially licensed NFT collections that have been released in collaboration with NFTStar (a sports fandom social platform with a web3 community) that are available for purchase on OpenSea.

[136][209] Son is part of UEFA's Real Scars campaign, which seeks to raise awareness of online abuse and harassment of football players.