Underwater simultaneous localization and mapping (SLAM) is essential for effectively navigating and mapping underwater environments; however, traditional SLAM systems have limitations due to restricted vision and the constantly changing conditions of the underwater environment. This study thoroughly examined the underwater SLAM technology, particularly emphasizing the incorporation of deep learning methods to improve performance. We analyzed the advancements made in underwater SLAM algorithms. We explored the principles behind SLAM and deep learning techniques, examining how these methods tackle the specific difficulties encountered in underwater environments. The main contributions of this work are a thorough assessment of the research into the use of deep learning in underwater image processing and perception and a comparison study of standard and deep learning-based SLAM systems. This paper emphasizes specific deep learning techniques, including generative adversarial networks (GANs), convolutional neural networks (CNNs), long short-term memory (LSTM) networks, and other advanced methods to enhance feature extraction, data fusion, scene understanding, etc. This study highlights the potential of deep learning in overcoming the constraints of traditional underwater SLAM methods, providing fresh opportunities for exploration and industrial use.