Born in Budapest, Adam Bogdan started his senior career with Hungarian Nemzeti Bajnokság I (Division One) team Vasas SC, embarking on a loan spell at Vecses in 2006. 

It was at Vecses where the Hungarian shot-stopper caught the attention of Bolton Wanderers scouts, with Bogdan touching down at The University of Bolton Stadium in 2007.

Spending two years progressing within the club's academy, Bogdan, then 21, was sent to League One club Crewe Alexandra on a temporary basis, however, he was confined to a single appearance for the Railwaymen.

Bogdan appeared for the Trotters, at senior level, for the very first time in August 2010, with the young goalkeeper keeping a clean sheet during a 1-0 victory over Southampton in the League Cup.

Just five days later, Bogdan made his Premier League debut, replacing Jussi Jääskeläinen who had been dismissed in the 38th minute.

He proceeded to feature four times in the league that season, with the next campaign seeing Bogdan rack up even more first-team minutes, with the Hungarian featuring 20 times, however, the Trotters were confined to relegation. 

Starting 41 and 29 games in the next two seasons respectively, Bogdan continued to hold the position and title of first-choice keeper at Bolton, with game time decreasing the next season. 

Upon the expiry of his contract with the then-Championship outfit, Bogdan joined Premier League giants Liverpool.

After four years of limited first-team opportunities, and loan spells with Wigan Athletic and Hibernian, Bogdan left the Reds.

Arriving on a permanent deal at Hibernian at the end of 2019, Bogdan was unable to make the starting XI in the league for the Scottish Premiership club. 

Ahead of the 2020/21 campaign, the 34-year-old joined Hungarian champions Ferencváros, with the experienced shot-stopper still with the club and is in a deputy role.