Durm began his club career in 1998 at the academy of SG Rieschweiler, before joining the academy of 1. Football Club Saarbrücken in 2008 where he became youth league top scorer of the 2009–2010 season with 13 goals. In July 2010, Durm was enrolled at the academy of 1.
FSV Mainz 05 on 4 December 2010 against SV Elversberg in the German Regionalliga.
In the 2011-2012 season, Durm succeeded to the second team of 1. FSV Mainz 05 and scored seven goals in 1.
FSV Mainz 05 II"s and his first 10 games. Then Durm went on to score two goals in a 1.
Following the scoring of nine goals in the first half of the 2011-2012 season, Durm scored four goals in the second half of the 2011-2012 season and in January 2012, both 1.
FSV Mainz 05 and Borussia Dortmund offered Durm a professional contract, but Durm declined the offer from 1. FSV Mainz 05 to sign with BVB. Borussia Dortmund
In the 2012-2013 season, Durm signed a contract with Borussia Dortmund until June 2014 and Durm was inducted into Borussia Dortmund II competing in the German third league. In the 2012-2013 3. Liga season, on 21 July 2012, Durm made his professional football debut in a game for Borussia Dortmund II against VfL Osnabrück.
Durm debuted in the Union of European Football Associations Champions League on 1 October 2013 in a 3–0 victory over French club Olympique Marseille.
At the start of the 2014-2015 season, Durm came on as a substitute in the 2014 DFL-Supercup. He scored his first Bundesliga goal in a 2-0 victory over Hertha Berlin on 9 May 2015.
Durm played in 2011 for both the German under-19 team and the German under-20 team And he debuted for the under-19 team on 31 May 2011, in a 3–0 victory against Hungary, and scored two goals.
On 12 November 2011, Durm debuted for the German under-20 team against Poland.
Durm debuted for the German under-21 team on 13 August 2013, in a 0–0 draw against France. Senior
On 1 June 2014, Durm debuted for the German senior team in a 2–2 draw against Cameroon at the Stadion im Borussia-Park in Mönchengladbach. He played 85 minutes before being substituted for Benedikt Höwedes.