Superconducting nanowire single photon detector (SNSPD) plays a significant role in plenty of fields such as quantum information, deep space laser communication and lidar, while the mechanism of the photon response process still lacks a recognized theory. It is prerequisite and essential for fabricating high-performance SNSPD to understand in depth and clarify the photon response mechanism of the SNSPD. As mature theories on the SNSPD response progress, hot-spot model and vortex-based model both have their disadvantages: in the former there exists the cut-off wavelength and in the later there is the size effect, so they both need further improving. The Cut-off wavelength means that the detection efficiency of the SNSPD drops to zero with the increase of light wavelength, which is indicated by the hot-spot model but not yet observed in experiment. The size effect implies that the vortex does not exist in the weak link with the width less than 4.41ξ, where ξ is the GL coherence length. Phase slip is responsible for the intrinsic dissipation of superconductors, which promises to expound the SNSPD photon response progress and to establish a complete theory. This paper reviews and discusses the fundamental conception, the development history and the research progress of the hot-spot models, i.e. the vortex-based model and the superconductor phase slips, providing a reference for studying the SNSPD photon response mechanism.