In recent years, underwater exploration for deep-sea resource utilization and development has a considerable interest. In an underwater environment, the obtained images and videos undergo several types of quality degradation resulting from light absorption and scattering, low contrast, color deviation, blurred details, and nonuniform illumination. Therefore, the restoration and enhancement of degraded images and videos are critical. Numerous techniques of image processing, pattern recognition and computer vision have been proposed for image restoration and enhancement, but many challenges remain. This survey presents a comparison of the most prominent approaches in underwater image processing and analysis. It also discusses an overview of the underwater environment with a broad classification into enhancement and restoration techniques and introduces the main underwater image degradation reasons in addition to the underwater image model. The existing underwater image analysis techniques, methods, datasets, and evaluation metrics are presented in detail. Furthermore, the existing limitations are analyzed, which are classified into image-related and environment-related categories. In addition, the performance is validated on images from the UIEB dataset for qualitative, quantitative, and computational time assessment. Areas in which underwater images have recently been applied are briefly discussed. Finally, recommendations for future research are provided and the conclusion is presented.