Volume holographic data storage is one of the most promising techniques to improve both the storage capacity of devices and the transfer data rate. Among the materials proposed as storage data media, azobenzene containing polymers have received much attention. Some of their properties seem to be suitable for holographic storage applications. However, they still present several problems, mainly those related with light sensitivity, response time and stability of the stored information. In this article we review the work performed on volume holographic storage using azobenzene containing polymers as well as the different approaches that have been proposed to overcome those problems.