Kampf's offensive numbers have never wowed anyone, either in his native Czech Republic. But the Chomutov, Czech Republic native's skills without the puck and as a penalty killer have made him a valuable teammate wherever he's played.

After the best of his five seasons in the Czech Extraliga (15 goals, 31 points in 52 games), Kampf opted to come to North America and signed as a free agent with the Chicago Blackhawks on May 2, 2017.

The 6-foot-2 center was assigned to Rockford of the American Hockey League for the 2017-18 season, called up by the Blackhawks on Dec. 27, 2017and made his NHL debut against the Vancouver Canucks the next night. He scored his first NHL goal against the Winnipeg Jets on Jan. 12, 2018.

Kampf became a regular in 2018-19, finishing with 19 points (four goals, 15 assists) in 63 games, and scored an NHL career-high eight goals, including his first two game-winners, in 70 games in 2019-20. He signed a two-year, $3 million contract with the Toronto Maple Leafs on July 28, 2021, and a four-year, $10 million contract June 28, 2023, after he had what was an NHL career-high 27 points in 2022-23.

Kampf signed a one-year, $1.1 million contract with the Vancouver Canucks on Nov. 15, 2025. He played for Team Czechia at the Olympic Winter Games Milano Cortina 2026 and was traded to the Washington Capitals on March 6, 2026.