Understanding crack propagation due to the presence of discontinuities in rock mass is vital in geotechnical engineering for predicting the stability of structures such as dams, tunnels, and foundations. Studying this process under both static and dynamic loading helps assess how a rock mass will behave and potentially fail, enabling safer designs and preventing disasters. In contrast to static loading, dynamic loading from earthquakes and explosions is complex and involves factors such as inertia and energy absorption, which significantly influence crack propagation in rock mass with discontinuities. This paper aims to review the impact of pre-existing defects or discontinuities on crack propagation in a rock mass under dynamic loading scenarios. The influence of several factors on the crack growth is reviewed, including the material properties of the rock (elasticity, strength, and toughness), loading conditions (magnitude, frequency, and duration of applied stresses) and geometric characteristics (intensity, orientation, bridge angle) of existing non-persistent discontinuities. This paper also discusses the effectiveness of various experimental studies for characterizing crack damage and deformation, such as digital image correlation (DIC), acoustic emission (AE), and 3D printing. Additionally, the effectiveness of numerical methods, such as Discrete Element Modelling (DEM), Particle Flow Method (PFM), Discrete Fracture Network (DFN), and hybrid methods, is reviewed for simulating crack growth and damage evolution. This review highlights the significance of accounting for loading circumstances and cracking features when predicting the behaviour of rock mass in engineering applications.