The use of compressive sensing in several applications has allowed to capture impressive results, especially in various applications such as image and video processing and it has become a promising direction of scientific research. It provides extensive application value in optimizing video surveillance networks. In this paper, we introduce recent state-of-the-art video compressive sensing methods based on neural networks and categorize them into different categories. We compare these approaches by analyzing the networks architectures. Then, we present their pros and cons. The general conclusion of the paper identify open research challenges and point out future research directions. The goal of this paper is to overview the current approaches in image and video compressive sensing and demonstrate their powerful impact in computer vision when using well designed compressive sensing algorithms.