<p>Non-line-of-sight (NLOS) propagation of radio signals can significantly impair the performance of wireless positioning systems in indoor environments. Therefore, accurately identifying and mitigating NLOS effects is essential for enhancing indoor positioning accuracy. Over the years, numerous algorithms have been proposed to address the bias introduced by NLOS conditions. This paper aims to provide an extensive survey of the existing NLOS identification and mitigation approaches in indoor environments and to highlight potential directions for future research. This paper first explores the influence of NLOS propagation on positioning accuracy, with particular attention to propagation delay bias, angle estimation errors, and the resulting degradation in system robustness and reliability. We then categorize NLOS identification approaches into statistical feature-based, geometry-based, machine learning (ML)-based, signal propagation model-based, and hybrid approaches. Furthermore, we analyze and summarize the strengths and weaknesses of each approach. Subsequently, we categorize NLOS error mitigation approaches into channel statistics-based, machine learning (ML)-based, filtering-based, map-based, weighting-based, least squares (LS), optimization-based, and hybrid methods. The merits and demerits of each NLOS mitigation approach are highlighted. Finally, we also explore important avenues for future research in the area of NLOS identification and mitigation in indoor environments.</p>