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Rock masses are heterogeneous materials containing a large number of discontinuities, and the failure of the natural rock mass is induced by the crack propagation and coalescence of discontinuities, especially for the rock mass around tunnel or underground space. Because the deformation or failure process of jointed rock mass exhibits strongly nonlinear characteristics, it is also very difficult to predict the strength and failure modes of the rock mass. Therefore, it is very necessary to study the failure mechanisms of jointed rock mass under different stress conditions. Apart from the stress condition, the discontinuities geometry also has a significant influence on the mechanical behavior of jointed rock mass. Then, substantial, experimental, and numerical efforts have been devoted to the study of crack initiation, propagation, and coalescence of rock or rock-like specimens containing different kinds of joints or fissures. The purpose of this review is to discuss the development and the contribution of the experiment test and numerical simulation in failure behavior of jointed rock or rock-like specimens. Overall, this review can be classified into three parts. It begins by briefly explaining the significance of studying these topics. Afterwards, the experimental and numerical studies on the strength, deformation, and failure characteristics of jointed rock or rock-like materials are carried out and discussed.