An overview of experimental study, computer simulations and theoretical models of fracture of nanocrystalline materials is presented. The key experimentally detected facts on ductile and brittle fracture processes are discussed. Special attention is paid to computer simulations and theoretical models of nucleation and growth of nanocracks and nanopores in deformed nanocrystalline materials. Also, we discuss mechanisms for fracture suppression in such materials showing good ductility or superplasticity.