Son came through the academy at FC Seoul, the same club that former Spurs defender Lee Young-pyo played for. Son was a ball boy in an FC Seoul home match in 2008 when he was a FC Seoul youth player. At that time, his role model was midfielder Lee Chung-yong, who played for Crystal Palace and Bolton Wanderers. Apart from his native language Korean, Son is also fluent in German and English. 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.

In August 2008, Son dropped out of Dongbuk High School (formerly FC Seoul U-18 Team) and joined Hamburger SV’s youth academy at age 16 through Korean FA Youth Project. A year later, he returned to South Korea. After participating in the FIFA U-17 World Cup, he formally joined Hamburger SV’s youth academy in November 2009

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. After scoring against Chelsea in August, he was out for two months due to a foot injury. He returned on 30 October 2010 to score his first league goal, against 1. FC Köln in the 24th minute. The goal made Son the youngest Hamburg player to score a goal in the Bundesliga at 18, breaking the record held by Manfred Kaltz.

On 24 December 2010, Son was named in South Korea national team’s squad for the 2011 AFC Asian Cup, making his debut for the national team in a pre-tournament friendly against Syria on 30 December. At the tournament finals, Son scored his first international goal during a 4–1 group stage defeat of India.

On 7 October 2011, after initially missing the first two matches of South Korea’s 2014 FIFA World Cup qualification campaign on 2 and 6 September 2011 due to an ankle injury, Son played in a friendly against Poland, and was again featured in 11 October World Cup qualifier against the United Arab Emirates. His selection for national team play was a point of concern for Son’s father, however, who caused a stir by asking the Korea Football Association not to select his son for the national team in the immediate future so he can rest and mature more as a player. Cho Kwang-rae, then the South Korea head coach, responded by saying that he would continue to call up Son when needed.

Son turned down the opportunity to participate in the 2012 London Olympics, opting to concentrate on his club career at Hamburger SV. Son was quoted as saying, “In Korea, an Olympic appearance has a special meaning, but I want to speed up for Hamburg. What matters is to pour all my time into team training.” Son did, however, play for the national team in the autumn of 2012 for two 2014 FIFA World Cup qualifiers against Lebanon and Iran, and became a regular call-up in friendlies and World Cup qualifying matches in 2013. In the World Cup qualifier against Qatar on 23 March 2013, Son came on as a substitute in the 81st minute and scored the winning goal in the 96th minute.

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. The 2012–13 season was a breakthrough season for Son as he scored two goals in an away fixture against Borussia Dortmund on 9 February 2013, helping his team to a 4–1 victory. Son was chosen Mann des Tages (Man of the Match) by kicker. On 14 April, Son netted two goals in a 2–1 win against Mainz 05. He finished the season with 12 goals, becoming the fifth South Korean footballer to achieve double digits in goals in Europe. He finished the 2012–13 season with 12 goals in 34 matches in all competitions.

On 13 June 2013, Bayer Leverkusen confirmed Son’s transfer for reportedly €10 million, which was the highest transfer fee in the club’s history at the time. He agreed to a five-year deal with the team. 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).

On 9 November 2013, Son scored a hat-trick for Leverkusen in a 5–3 win against his former club Hamburgers SV. On 7 December, Son scored a crucial goal against Borussia Dortmund to put his club just four points off the summit of the Bundesliga. On 10 May 2014, Son scored another goal against Werder Bremen ensuring his team a spot for the 2014–15 UEFA Champions League. He finished the 2013–14 season with 12 goals in 43 matches.

In June 2014, Son was named in South Korea’s squad for the 2014 World Cup. On 22 June, he scored in a 4–2 defeat to Algeria in the team’s second group match. The Korea Football Association requested Bayer Leverkusen to allow Son to play in the 2014 Asian Games, as winning the gold medal at the tournament would grant Son exemption from military service. Despite Son affirming his interest and the KFA’s efforts, his club at the time, Bayer Leverkusen, refused to release him, as his absence would mean the team would lose him for at least six matches.

Son scored a hat-trick against VfL Wolfsburg on 14 February 2015, in a 4–5 defeat, scoring when they were losing 0–3. He finished the 2014–15 season with 17 goals in 42 matches.

On 28 August 2015, Son joined Premier League club Tottenham Hotspur for £22 million (€30 million) on a five-year contract, subject to work permit and international clearance. Upon his signing, he became the most expensive Asian player in football history. The record had been held since 2001 by Japanese Hidetoshi Nakata, who transferred from Roma to Parma for €25 million.

On 3 September 2015 at the Hwaseong Stadium, Son scored a hat-trick in an 8–0 home win over Laos in the second round of qualification for the 2018 World Cup.

Before the season, he reportedly asked Spurs manager Mauricio Pochettino for permission to leave Tottenham in an attempt to get more playing time, but was instead given a chance to fight for his place at Spurs. On 10 September 2016, Son scored two goals and created a third in his first appearance of the season, in a 4–0 win against Stoke City. Son followed that performance up with a second brace, coming at Middlesbrough on 24 September, earning his team a 1–2 victory. Upon equalling his league goal total from the previous season in 25 fewer matches, Son was hailed by Pochettino as “a different person – he’s more mature and he knows the league and he’s settled in fantastically now.” Son continued his excellent run of form with his fifth goal in five matches on 27 September in the Champions League. Playing at CSKA Moscow, Son slipped a shot past goalkeeper Igor Akinfeev for the only goal of the match. On 14 October, Son was named the Premier League Player of the Month for September, being the first South Korean and first Asian to receive the award.

In June 2016, Son was named as an over-age player in South Korea’s squad for the 2016 Summer Olympics. Son amassed two goals in the group stages with a goal against Fiji and another against Germany, helping his team to top the group with two wins and a draw. South Korea was eliminated by Honduras in the quarterfinals, with Son missing crucial chances.

Following the Christmas break Son continued to score the odd goal over the following couple of months and then on 12 March 2017 he scored his first Spurs hat trick in the FA Cup against Millwall in a 6–0 win. 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. He scored in the 2–0 victory away at Burnley on 1 April 2017, and four days later he scored in the 91st minute to put Spurs ahead at Swansea, in a game where they were losing 1–0 after 88 minutes and ended up winning 3–1. A brace at home to Watford the following weekend brought his season total to 18 goals, 11 in the Premier League, his best ever goals return. On 12 May 2017, Tottenham announced that Son had won the Premier League Player of the Month for April, the second time of his career and thus becoming the only player in 2016–17 to win the award 2 times. On 18 May 2017, Son bagged a brace away to Leicester City as part of a 6–1 rout of their former title rivals. With 21 goals in all competitions, Son joined Harry Kane and Dele Alli as the first trio of Spurs players with over 20 goals on the season.

Son scored his first goal of the 2017–18 season in the UEFA Champions League game against Borussia Dortmund on 13 September 2017 at Spurs temporary home Wembley Stadium, which Spurs won 3–1. He scored his first Premier League goal of the season when Spurs beat Liverpool 4–1 at home. On 5 November 2017, Son scored the only goal in the 1–0 win against Crystal Palace. The goal brought his tally in the Premier League to 20 and in doing so he became the top Asian goalscorer in Premier League history, breaking the record set by Park Ji-Sung at Manchester United. On 13 January 2018, Son scored a goal and provided an assist in a game against Everton, matching the club record set in 2004 by Jermain Defoe of scoring in five consecutive home games. On 28 February 2018, Son scored a brace and assisted Fernando Llorente as Tottenham beat Rochdale 6–1 in the 5th Round of the FA Cup. Son also converted a penalty, but his goal was overruled by the video assistant referee. Son has become the first Asian to finish the season as a top-10 goal scorer in the English Premier League.

On 13 June 2017, Son broke his right forearm after falling awkwardly on his arm during a World Cup qualifier match in Doha against Qatar. He was part of the team that saw Korea qualify for the 2018 World Cup after a 0–0 draw against Uzbekistan on 5 September 2017. On 4 June 2018, Son was selected in 23-man squad for the World Cup. 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. 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.

On 20 July 2018, Son signed a new five-year deal extending his contract with Tottenham until 2023. The first goals of the season came in October 2018 when he scored a brace in his 150th game for Tottenham in the 2018–19 EFL Cup match against West Ham. He scored his first league goal of the season, his 50th goal for the club in all competitions, in a solo effort in the 3–1 home win against Chelsea, inflicting the first defeat for Chelsea in the Premier League this season. This goal won the Premier League’s Goal of the Month award for November. On 13 February 2019, Son scored the first goal in a 3–0 win over Borussia Dortmund, in the first leg of the round of 16, UEFA Champions League. At the end of the month he was named Premier League Player of the Year at the London Football Awards. On 3 April 2019, Son scored the very first professional goal at the new Tottenham Hotspur Stadium in a 2–0 victory over Crystal Palace.

On 9 April 2019, Son scored the very 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. In the return leg, Son scored twice to earn Tottenham a 4–4 aggregate win on the away goals rule and help the club reach the semi-finals of the competition for the first time since 1962, and only the second time ever. 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. On 4 May 2019, Son received his first red card in the Premier League due to his vindictive action against Jefferson Lerma.

Son opened his 2019–20 account on 14 September 2019 by scoring two goals against Crystal Palace in the Premier League with a final result of 4–0. On 21 October, Son was named in the 30-man shortlist for the 2019 Ballon d’Or. 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. The injury prompted great concern and anguish from the players and supporters; Son was visibly highly distressed by the incident. Following a red card for a challenge on Gomes, Son also received suspension for three Premier League games. 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. The FA accepted the appeal and Son’s red card was rescinded on 5 November. 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.

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. On 7 December, Son ran from one end of the pitch to the other, going past seven Burnley players, to score an individual goal that was labelled a goal of the season contender. The nature of the goal saw Mourinho dub him “Sonaldo Nazario” in reference to the type of goal former Brazilian international Ronaldo would score. On 22 December 2019, facing Chelsea, Son was sent off after raising his boot against Antonio Rüdiger’s ribs. In January 2020, Son was awarded the Premier League goal of the month for December for his goal against Burnley, eventually winning him the Goal of the Season award as well. On 16 February 2020, Son scored two goals at Villa Park and earned a 3–2 victory for Tottenham, in which he became the first Asian footballer to score 50 goals in the Premier League, with 51 scored goals in 151 Premier League matches. Son played the full game despite suffering a fracture to his arm at the 31st second of the game. 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.

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. After completing a two-week quarantine on his return to Korea, he served with the Marine Corps for three weeks on Jeju Island.

Son used the suspension of football during the COVID-19 pandemic to complete South Korean mandatory military service. He was exempted from military service with a gold medal at the Asian Games, but he had to do military basic training regardless of exemption. He completed basic training in the Republic of Korea Marine Corps in Jeju in April–May 2020, finishing in the top five of 157 trainees.