Abstract: The "three relations (rock constitutive equation, crack-wave interaction, superposition effect between blast waves and explosion gas)" of rock blasting are the important contents of the blasting theory. The interaction between blast wave and crack is the key factor affecting the rock fragmentation. Focuses on the four aspects, namely, the interaction between blast waves and stationary crack, the interaction between blast waves and blast induced crack, the interaction among cracks under the action of blast waves, and the propagation behavior of cracks under the superposition of geo-stress and blast waves, this paper systematically reviews the progress in the study of the interaction mechanism between blast waves and cracks under rock blasting. At present, it is found that blast waves reflect and diffract when it encountered stationary crack, resulting in the "double Mach cone" phenomenon, which causes more explosive energy to accumulate around the stationary cracks, inducing damage and destruction around the crack. Furthermore, using photo-elastic experiment, we found that the dilatational wave suppresses the propagation of oppositely propagating crack, while the shear wave promotes the propagation of the oppositely propagating crack. However, during the interaction between blast waves and same propagating blast induced crack, the dilatational wave promotes the propagation of same propagating crack, and the shear wave suppresses the propagation of the same propagating crack. Additionally, under the double borehole blasting, the two opposite propagating cracks interact between each other, causing “linking effect” and forming an interconnected shape. Last but not least, the geo-stress can promote the propagation of blast induced crack parallel to the direction of the maximum principal stress and suppress the propagation of blast induced crack perpendicular to it. Moreover, the greater the difference in principal stresses in the geo-stress field, the longer the propagation length of blast induced cracks along the direction of the maximum principal stress. Based on the above analysis, this paper looks forward to the development of the research on the interaction mechanism between blast waves and cracks.