Dynamic compressive sensing is an extension of traditional static compressive sensing to dynamic signals, which has a wide application in MRI, video compressive sensing and target tracking. Since dynamic signals are usually sparse in some transformed matrices and change slowly with time varying, an underdetermined measurement matrix can be used to compress the signals. The research of dynamic compressive sensing mainly focuses on three parts: Sparse representation of dynamic signals, dynamic compressive measurement, and reconstruction of dynamic signals. A comprehensive survey about dynamic compressive sensing is given in this article. At first, the basic concept of dynamic compressed sensing is introduced, which includes several mathematic models of dynamic signals, sparse dictionary learning algorithms and methods of adaptive measurement. Secondly, we classify the reconstruction algorithms into two main parts: Least square based algorithms and Bayesian algorithms, and we also introduce some representative algorithms in detail from each part. Finally, several applications of dynamic compressed sensing are introduced, and we provide a reference for further investigation on reconstruction algorithms.