One of the major heavy fighter designs was the Messerschmitt Bf 110, a pre-war German design that the Luftwaffe considered to be more important than their single engine fighters. It was expected that the 110 would be able to escort bombers on missions at long range, using its superior speed to outrun defending interceptors which would outmanuver it. The 110 proved capable of this sort of mission for only a short time, it served well against the Hawker Hurricane during the Battle of France, but was hopelessly outperformed by the Supermarine Spitfire it faced during the Battle of Britain. The 110 was later re-used as a night fighter and bomber destroyer, where it served until near the end of the war.
Many heavy fighter designs were actually converted bombers. In particular one of the most successful heavy fighters was the Bristol Beaufighter, a conversion of their earlier Beaufort torpedo bomber.
Although there are numerous fighter designs that could be classified as heavy fighters, in general the term is no longer used.