Abstract: This paper describes the background of matrix completion firstly, points out the mathematics model of matrix completion, analyzes the low rank property and the incoherence property in matrix completion. Mainly introduces three reconstruction algorithm commonly used in matrix completion: SVT(Singular Value Thresholding)、ADMiRA(Atomic Decomposition for Minimum Rank Approximation)and SVP(Singular Value Projection), compares their reconstruction performance in this paper. Secondly, we analyze the connection between matrix completion and compressed sensing. Finally we introduce the application of matrix completion in collaborative filtering, system identification, sensor network, image processing, sparse channel estimation, spectrum sensing and multimedia coding and communication.