Light fields can completely capture light information in three-dimensional space, thus enabling the intensity of light at different positions and directions to be recorded. Consequently, complex dynamic environments can be perceived accurately, thus offering significant research value and application potential in fields such as life sciences, industrial inspection, and virtual reality. During the capture, processing, and transmission of light fields, limitations in equipment and external factors, such as object motion, noise, low lighting, and adverse weather conditions, can distort and degrade light-field images. This significantly compromises the quality of the images and restricts their further applications. Hence, researchers have proposed restoration and enhancement algorithms for various types of light-field degradations to improve the quality of light-field images. Classical light-field image restoration and enhancement algorithms rely on manually designed priors and exhibit disadvantages of high complexity, low efficiency, and subpar generalizability. Owing to the advancement of deep-learning technologies, significant development has been achieved in algorithms for light-field image restoration and enhancement, thus significantly improving their performance and efficiency. In this survey, we introduce the research background and representation of light fields as well as discuss the typical algorithms used for addressing different light-field degradations, with emphasis on spatial and angular dimension super-resolution, denoising, deblurring, occlusion removal, rain/haze/snow removal, reflection removal, and low-light enhancement. We conclude this survey by summarizing the future challenges and trends in the development of light-field image restoration and enhancement algorithms.