The neural radiation field (NeRF) has significant advantages in generating high-fidelity maps thanks to its neural implicit representation-based scene. The application of NeRF in simultaneous localization and mapping (SLAM), namely the NeRF-based SLAM method, enables continuous 3D modeling while achieving high-precision localization to enhance the quality and detail of the scene reconstruction by rendering new perspectives and predicting unknown regions. To track the latest research results in this field, this study reviews and summarizes the key algorithms of NeRF-based SLAM in recent years. Firstly, the core principle of NeRF technology is introduced and a comprehensive overview of the framework of NeRF-based SLAM methods is given, followed by focusing on the improvements and optimizations of NeRF-based SLAM, including improving the efficiency of neural implicit representation, solving the large-scale scene building problem, adding loopback and global optimization to achieve global consistency and solving the dynamic interference problem. Finally, an outlook on the NeRF-based SLAM method is presented to provide valuable references for related researchers to promote more innovative research.