Neural Radiance Fields (NeRF) have emerged as a powerful paradigm for 3D scene representation, offering high-fidelity renderings and reconstructions from a set of sparse and unstructured sensor data. In the context of autonomous robotics, where perception and understanding of the environment are pivotal, NeRF holds immense promise for improving performance. In this paper, we present a comprehensive survey and analysis of the state-of-the-art techniques for utilizing NeRF to enhance the capabilities of autonomous robots. We especially focus on the perception, localization and navigation, and decision-making modules of autonomous robots and delve into tasks crucial for autonomous operation, including 3D reconstruction, segmentation, pose estimation, simultaneous localization and mapping (SLAM), navigation and planning, and interaction. Our survey meticulously benchmarks existing NeRF-based methods, providing insights into their strengths and limitations. Moreover, we explore promising avenues for future research and development in this domain. Notably, we discuss the integration of advanced techniques such as 3D Gaussian splatting (3DGS), large language models (LLM), and generative AIs, envisioning enhanced reconstruction efficiency, scene understanding, decision-making capabilities. This survey serves as a roadmap for researchers seeking to leverage NeRFs to empower autonomous robots, paving the way for innovative solutions that can navigate and interact seamlessly in complex environments.