[5][6][7] Widely regarded as one of the greatest players of his era,[8][9][10] Müller has been praised for his positioning, finishing, playmaking, work-rate, and consistency in both scoring and creating goals.

[13] Müller played as a youth for TSV Pähl, and at the age of 10[14] he made the 50-kilometre (31 mi) journey to join local Bundesliga side Bayern Munich in 2000.

[16] Müller made his debut for the reserve team in March 2008 when he replaced Stephan Fürstner in a Regionalliga match against SpVgg Unterhaching,[17] in which he scored.

[21] Müller became involved in the first-team under then manager Jürgen Klinsmann; he appeared in pre-season friendlies,[22][23] and made his full debut on 15 August 2008, when he came on as a substitute for Miroslav Klose for the last ten minutes of a Bundesliga match against Hamburger SV.

[26] In February 2009, Müller signed his first contract for the senior team, a two-year deal effective from the 2009–10 season, along with reserve teammate Holger Badstuber.

[30] He rounded off September by being named the Bundesliga Player of the Month[31] and earned praise from his namesake, legendary former Bayern and Germany striker Gerd Müller.

[36] During the second half of the season, Müller continued to be a regular first-team starter,[28] usually playing in a central striking role due to the availability of other wide players Franck Ribéry and Arjen Robben.

[67] Müller's mentor Van Gaal was increasingly criticised for inflexibility in tactical, transfer and selection policy,[68] and ultimately lost his job, being replaced with Jupp Heynckes.

[76][77] On 19 May 2012, Müller scored the opening goal in the 83rd minute of the Champions League final against Chelsea with a powerful header, before being substituted for defender Daniel Van Buyten moments later.

Müller stated post match how dissatisfied he was about the amount of time he had spent on the bench recently,[78] although also expressed his desire to stay at Bayern in spite of this.

[80] On 2 September, he netted a brace as Bayern thrashed southern rivals VfB Stuttgart, 6–1, in front of 71,000 at the newly expanded Allianz Arena.

Müller tapped in his fifth goal of the Champions League campaign on 2 April, completing a 2–0 first leg defeat of Juventus in the quarter-finals, ending the Italian club's 18-match unbeaten record in Europe.

[87] On 23 April 2013, Müller scored two goals and gave an assist in a 4–0 win against Barcelona in the first leg of the Champions League semi-finals at the Allianz Arena.

[88] In the return fixture at the Camp Nou, Müller scored a header as Bayern won 3–0 to hand Barcelona their biggest ever aggregate defeat in the Champions League, with a 7–0 scoreline across the two matches.

On 1 June, Müller scored a penalty in the final of the 2012–13 DFB-Pokal as Bayern won the cup 3–2 against VFB Stuttgart to complete a historic treble.

On 17 May 2014, He scored Bayern's second goal in a 2–0 extra-time defeat of Borussia Dortmund in the 2014 DFB-Pokal Final, giving die Roten the tenth league and cup double in their history.

[105] On 11 March 2015, Müller scored two goals against Shakhtar Donetsk in a 7–0 win[107] to draw level with former teammate Mario Gómez as the top-scoring German player in UEFA Champions League history.

[131] On 3 May 2016, Müller had a penalty kick saved by Jan Oblak in the Champions League semi-final second leg at home to Atlético Madrid.

On 18 August 2023, Müller came off the bench in the 84th minute in a 4–0 away win over Werder Bremen in the opening match, in which he managed to participate in 16 Bundesliga seasons to become the first player to achieve this feat at the club.

[175][176] On 30 April, he played his 150th Champions League match in a 2–2 draw against Real Madrid in the semi-finals, becoming the third player to achieve this feat with one club, following Xavi and Iker Casillas.

[182][183][184] On 17 September, he featured in his 152nd Champions League match which ended in a 9–2 victory over Dinamo Zagreb, breaking previous record of Xavi as the player with most appearances for one club in the competition.

[202] Despite suffering a scare when he fell off his bicycle at the team's training camp in South Tyrol,[203] Müller only received superficial injuries and made the final cut for the tournament when the squad was reduced to 23 players.

[205] He earned his second international cap in the final warm-up match before the World Cup when he came on as a half-time substitute for Piotr Trochowski in a 3–1 win over Bosnia and Herzegovina.

Müller did not manage to score a goal as Germany crashed out of the World Cup at the group stage for the first time since 1938 following a shock loss to South Korea.

[241] On 5 March 2019, national team coach Joachim Löw confirmed that he would plan without Müller for the foreseeable future, along with his club teammates Jérôme Boateng and Mats Hummels.

[243] However, after Löw later admitted in March 2021 that he was considering reversing his decision and allowing the previously barred players to partake in the upcoming UEFA Euro 2020, Müller insisted he was "definitely ready" to return to international duty, stating his desire to win another title with Germany.

[244] On 19 May 2021, Müller, along with Hummels, was included in Germany's final 26-man squad for UEFA Euro 2020, ending a period of over two years of exclusion from the national team.

[57] Müller is heavily involved in buildup play[262] and he has been praised by the media for his intelligent movement off the ball;[258][263] he describes himself as a player who can find spaces in the opposition defence but not particularly good at dribbling or one-on-ones.

During the 2014 FIFA World Cup, Germany manager Joachim Löw stated that Müller "is a very unorthodox player and you can't really predict his lines of running, but he has one aim and that is 'how can I score a goal?'".

[11][267][268] Former Bayern assistant coach Hermann Gerland gave him the nickname Radio Müller for his loud and frequent comments on the pitch and in the dressing room.