Brillouin dynamic grating (BDG) based on stimulated Brillouin scattering effect has been extensively investigated globally. Compared with fiber Bragg grating (FBG), BDG has many advantages, such as fast reconstruction, read-write separation, and parameter control. It has been realized in polarization-maintaining, single-mode, low-mode, and photonic crystal fibers. Simultaneously, different types of BDG research, such as chirped BDG, phase-shifted BDG, chaotic BDG, and random BDG, are constantly emerging. This paper briefly introduces the generation principle of BDG and gives a detailed overview of different BDG fibers, different types of BDG, and BDG application in distributed fiber sensing and all-optical signal processing. Finally, the development trend of BDG is summarized and prospected.