Non-blind image restoration is one of the most improtant research topics in the field of computer vision. It is also a typical ill-posed problem in mathematics. Its goal is to estimate a clear image from a blurred image when the point spread function is known. Its research focuses on how to make an appropriate compromise between improving clarity and suppressing noise. In the past 50 years, non-blind image restoration has made great progress. From the Wiener filtering to deep learning based methods, scholars have proposed hundreds of non-blind image restoration algorithms and applied them in various academic fields. This paper first introduces the basic concept and research significance of non-blind image restoration, then classifies and summarizes the main non-blind image restoration algorithms according to the algorithm attributes, which are generally divided into traditional methods and deep learning based methods. The traditional methods are divided into the direct method and iterative method, then are analyzed for their advantages and disadvantages. The performance of representative restoration algorithms is compared in a varity of typical experiments. Finally, the development trend and important research directions of non-blind image restoration algorithms are proposed.