In Exposaurus, natural history museums compete to assemble the most sensational exhibits of dinosaur fossils and gems. As the museum directors, players send explorers to start new excavations and recover findings that should be part of the museum collection.

Each exploration, however, results in an explorer leaving that player's museum to work at the national museum, which means the possibilities for the museum tighten in future turns.

The size and type of the collections determines which museum director comes out on top.