[1] Growing up in Goldberg, he frequently visited the local movie theater, later citing it as an influence on his decision to become an actor.

[2] He won the German Film Award for Best Actor, as well as the Deutscher Schauspielpreis [de] (German Actor Award), for the 2015 film A Heavy Heart in which he played Herbert, a boxer diagnosed with amyotrophic lateral sclerosis (ALS).

[5][6] Kurth prepared extensively for the role, gaining 35 pounds (16 kg) in the months before filming to physically resemble a former boxer, before losing his newly gained weight over the course of the 35-day shoot to portray Herbert's ALS progression.

[7] Scott Roxborough of The Hollywood Reporter called Kurth's portrayal of Herbert an "acting master class".

[7] In 2018, Kurth was nominated for the Deutscher Fernsehpreis award for Best Actor, for his role as Detective Bruno Wolter in the German neo-noir television series Babylon Berlin.