Atomically thin films, such as graphene, graphene oxide, hexagonal-boron nitride (h-BN), and molybdenum disulfide (MoS2), have attracted intensive studies to explore their properties and potential applications as next generation materials due to their outstanding mechanical, electrical, thermal, and optical properties. The study of the mechanical behavior of this class of materials is in particular interesting as it not only physically determines the potential application fields where these materials can be utilized but also has revealed unique mechanical size effects and phenomena. Researchers have been studying the mechanical properties such as elastic modulus, strength, friction, and fracture behavior of atomically thin films for over a decade now. Here, we review recent results of the mechanical characterization and understanding of this class of materials.