Küng won the individual pursuit at the 2015 UCI Track Cycling World Championships, after beating Jack Bobridge in the final.

In the 2015 Tour de Romandie, he grabbed the biggest victory of his career at that point in solo fashion.

On a cold rainy day, he was part of the early breakaway and dropped his fellow escapees some 30 kilometres (19 mi) before the line, resisting to their return while riding toward victory in Fribourg.

[6] Küng won his first Grand Tour stage at the 2024 Vuelta a España on the final stage of the race, beating out race leader Primož Roglič in the time trial by a comfortable 31 seconds.

[7] He is scheduled to compete in the time trial at the 2024 UCI Road World Championships in his home country of Switzerland.