Photodeformable azobenzene (azo) polymers are a class of smart polymers that can efficiently convert light energy into mechanical power, holding great promise in various photoactuating applications. They are typically of crosslinked polymer networks with highly oriented azo mesogens embedded inside. Upon exposure to the light of appropriate wavelength, they experience dramatic order parameter change following the configuration change of the azo units. This could result in the generation and accumulation of the gradient microscopic photomechanical force in the crosslinked polymer networks, thus leading to their macroscopic deformation. So far, a great number of photodeformable azo polymers have been developed, including some unoriented ones showing photodeformation based on different mechanisms. Among them, photodeformable azo polymers with dynamic crosslinking networks (and some uncrosslinked ones) have aroused particular interest recently because of their obvious advantages over those with stable chemical crosslinking structures such as high recyclability and reprocessability. In this paper, I provide a detailed overview of the recent progress in such reprocessable photodeformable polymers. In addition, some challenges and perspectives are also presented.