One highly focused research direction in neural rendering is the neural radiance field (NeRF), which offers a novel implicit representation of three-dimensional scenes. NeRF conceptualizes the scene as a medium comprising numerous luminescent particles and applies a differentiable volume rendering equation to aid virtual cameras in rendering corresponding scene images. Its implicit and differentiable characteristics confer remarkable advantages on NeRF, particularly in the field of new viewpoint synthesis. This review thoroughly examines the latest research progress of NeRF in the domain of new viewpoint synthesis. Moreover, this study comprehensively analyzes how NeRF addresses unbounded scenes, dynamic environmental scenes, and sparse viewpoint scenes in practical applications, along with its advancements in training and inference acceleration. Concurrently, this study highlights NeRF’s challenges in this task and presents a vision for future research.