Jung played his first Bundesliga match for Eintracht Frankfurt, and first fully professional game, on 8 March 2009 in a 0–0 draw against Arminia Bielefeld, as a substitute for Patrick Ochs. On 7 February 2010, he scored his first Bundesliga goal at Signal Iduna Park against Borussia Dortmund. He became a regular in the Frankfurt first team during the 2010–11 season, during which they were surprisingly relegated from the Bundesliga, but was almost ever-present the following season as they bounced back at the first attempt. He extended his contract on 4 April 2013 until 30 June 2015. He joined VfL Wolfsburg on 22 May 2014 and signed a contract until 30 June 2018. Although he was still under contract with Frankfurt, Wolfsburg could acquire his services by fulfilling a release clause in the amount of €2.5 million. His annual salary at Wolfsburg is believed to be €4 million. On 23 June 2019, Jung joined Hannover 96 on a 1-year contract.
International career
On 11 November 2012, Jung was first called up to the German senior squad, following injury related withdrawals by several players, including Holger Badstuber and Jérôme Boateng, before a friendly against Netherlands on 14 November 2012. He is the first Eintracht Frankfurt player to be called up to the national team since Horst Heldt in 1999. Nevertheless, he did not play in the match. Almost two years later, in May 2014, he was called up for the second time. In a 0–0 draw in a friendly against Poland in Hamburg he made his debut by being substituted in the 71st minute for fellow debutant Kevin Volland. Originally this match was scheduled as a test for the 2014 FIFA World Cup. But unfortunately its date collided with the DFB-Pokal final between FC Bayern Munich and Borussia Dortmund, the FA Cup Final including Arsenal and the Champions League final including Real Madrid. The players of these four teams made up the vast majority of the regular German squad at that time. Consequently, only ten of the 30 nominated players of the preliminary world cup squad were available and in the end twelve players made their debuts in the match.
