Various failure criteria for rocks are discussed with emphasis on intrinsic temporal and structural features. It is shown that such internal-time/structure-based fracture criteria are different expressions of the governing structural changes under external action. Rock mass has a complex internal structural hierarchy, and failure is intimately related to the development of cracks, their growth and coalescence. In order to describe properly deformation and fracture in rocks it is necessary to consider the internal structural hierarchy of the rock mass and the finiteness of crack propagation. Critical issues including the essence of incubation time, the nature of limit failure strain, and the type of failure criteria for different strain rate sensitivity regimes, are discussed.