Non-line-of-sight (NLoS) imaging is a promising technique developed in recent years, which can reconstruct hidden scenes by analyzing the information in the intermediate surface, and "see around the corner", and has strong application value in many fields. In this paper, we review the reconstruction algorithm for NLoS imaging tasks. Firstly, considering the crossover and non-independent phenomena existing in the NLoS imaging classification, we use the different features of physical imaging models and algorithm models to reclassify them. Secondly, according to the proposed classification criteria, we respectively review the traditional and deep learning-based NLoS imaging reconstruction algorithms, summarize the state-of-the-art algorithms, and derive the implement principle. We also compare the results of deep learning-based and traditional NLoS imaging reconstruction algorithms for reconstruction tasks. Finally, the current challenges and the future development of NLoS imaging are summarized. Different types of NLoS imaging reconstruction algorithms are comprehensively analyzed in this review, which provides important support for the further development of NLoS imaging reconstruction algorithms.