The indoor localization algorithm with non-line-of-sight (NLOS) is studied. Firstly, we describe the techniques widely used in indoor localization and algorithms (dead reckoning, fingerprint identification, adjacent to detect, orientation of the pole, triangulation, multilateral, centroid localization), and summarize the principle, advantages, disadvantages and applicable scenario. Secondly, the necessity of studying NLOS identification and mitigation is illustrated by simulation test. Then, several algorithms of NLOS identification and mitigation are introduced respectively. NLOS identification algorithms include statistical method, geometric relation method, machine learning method, channel feature extraction method and virtual point density recognition method. Moreover, NLOS mitigation algorithms include fuzzy theory method, introduced equilibrium parameter method, geometric relation method, wavelet denoising method, machine learning method, convex optimization method, residual method, least square method and multidimensional scaling method. Finally, this paper summarizes the whole paper and points out the problems to be solved in NLOS indoor localization.