They first appeared during the Paleozoic, but began to flourish only during the Mesozoic. The biggest was about a size of an adult Eusthenopteron.
The ammonites began to decline at the end of the Cretaceous, and died-out during the K-T extinction alongside the dinosaurs, the giant marine reptiles like Mosasaurus, and others. The main theory is that unlike the modern Nautilus, which lays several smaller clutches of eggs on the sea floor, the ammonites had only one big clutch of eggs during the lifetime, and their young lived in the upper waters of the seas, alongside other plankton - and died-out alongside it when the meteorite hit.
List of Ammonites
In Popular Culture
Ammonite appears in Jurassic World: The Game as a legendary aquatic creature, alongside the Baculites, in which it is a super rare aquatic creature.