Stranger Things - New Mutants

In 2015, Heaton made his acting debut with the ITV crime drama series DCI Banks, playing the role of Gary McCready. Then he appeared as Riley in ITV's detective series Vera.

He guest starred in BBC One's medical drama series Casualty as Jason Waycott. In 2016, he appeared in the thriller film Shut In, co-starring Naomi Watts and Oliver Platt, and directed by Farren Blackburn. Heaton also plays Jonathan Byers in the Netflix supernatural drama series Stranger Things.

In May 2017, Heaton was cast to star as Samuel "Sam" Guthrie / Cannonball in New Mutants, a 2019 film based on the Marvel Comics comic book of the same name.

In August 2018 it was announced that Heaton would be playing Joseph Merrick (The Elephant Man) in a new two-part BBC drama, a decision which has drawn criticism from some quarters.