He is a two-time major singles quarterfinalist, making him by far the most successful male tennis player in Luxembourgish history.

Following an early exit at the Junior French Open, He reached the final of the Boys' Singles at the 2001 Wimbledon Championships, where he was defeated by Roman Valent of Switzerland (6–3, 5–7, 3–6).

He made his ATP debut at the 2002 Rosmalen Grass Court Championships after receiving a wildcard into the singles main draw where he lost in the first round to Ivo Heuberger (2–6, 6–3, 6–7(8–10)).

His breakthrough event came at the 2004 Legg Mason Tennis Classic where he made his first ATP Tour final and defeated 1st seed and world No.

He made his second ATP Tour final at the 2005 Los Angeles Open where he lost to top seed and world No.

He started to get worse results in ATP events which dropped his ranking back outside of the top-100 to 105 by the end of the year.

He reached the main draw and advanced to the quarterfinals of a Grand Slam tournament for the first time in his career, earnining a win over fifth-seeded Nikolay Davydenko in the fourth round.

On 19 January 2009, Müller beat Spaniard Feliciano López (6–3, 7–6, 4–6, 4–6, 16–14) in an epic four-hour, 24-minute match in the first round of the 2009 Australian Open.

[4] Müller's final match in 2013 was at the 2013 French Open where he lost in round 1 to Roberto Bautista Agut.

[5][6] In January, Müller returned to playing tennis and competed mostly on the Challenger Tour, winning five titles.

Müller began 2015 at the Aircel Chennai Open, where he made the quarterfinals, losing to eventual champion Stan Wawrinka.

[6] He had a strong showing in Rotterdam, defeating David Goffin and Grigor Dimitrov, and then lost to Wawrinka in the quarterfinals.

Müller had a strong start to the grass court season, reaching the semifinals of the Topshelf Open as well as the quarterfinals at Queen's, beating defending champion Dimitrov for the second time in two meetings since the beginning of the year.

At the 2016 Ricoh Open, he reached the final, losing to the defending champion Nicolas Mahut in straight sets.

He advanced to the final of the Hall of Fame Tennis Championships, losing to second-seeded Ivo Karlović in three sets.

At the 2016 Swiss Indoors, Müller defeated Grigor Dimitrov in the first round and then went on to reach the semifinals, falling to Kei Nishikori in three sets.

This came less than a week after he lost in the men's doubles final of the 2017 Brisbane International, playing alongside Sam Querrey.

Müller entered an ATP tournament as a defending champion for the first time in his career at the 2018 Sydney International, ousting John Millman before subsequently losing to Benoît Paire.

[9] He played his last match on the ATP World Tour at the 2018 US Open, losing in a five-setter to Lorenzo Sonego in the first round.

[10] Müller was honored as one of the biggest retirees of the year at the 2018 ATP Finals alongside Florian Mayer and André Sá.

He competed in 30 ties and out of 73 matches, he won 56 and lost 17, which made him Luxembourg's most successful Davis Cup player.