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The underwater domain presents unique challenges and opportunities for scientific exploration, resource extraction, and environmental monitoring. Autonomous underwater vehicles (AUVs) rely on simultaneous localization and mapping (SLAM) for real-time navigation and mapping in these complex environments. However, traditional SLAM techniques face significant obstacles, including poor visibility, dynamic lighting conditions, sensor noise, and water-induced distortions, all of which degrade the accuracy and robustness of underwater navigation systems. Recent advances in deep learning (DL) have introduced powerful solutions to overcome these challenges. DL techniques enhance underwater SLAM by improving feature extraction, image denoising, distortion correction, and sensor fusion. This survey provides a comprehensive analysis of the latest developments in DL-enhanced SLAM for underwater applications, categorizing approaches based on their methodologies, sensor dependencies, and integration with deep learning models. We critically evaluate the benefits and limitations of existing techniques, highlighting key innovations and unresolved challenges. In addition, we introduce a novel classification framework for underwater SLAM based on its integration with underwater wireless sensor networks (UWSNs). UWSNs offer a collaborative framework that enhances localization, mapping, and real-time data sharing among AUVs by leveraging acoustic communication and distributed sensing. Our proposed taxonomy provides new insights into how communication-aware SLAM methodologies can improve navigation accuracy and operational efficiency in underwater environments. Furthermore, we discuss emerging research trends, including the use of transformer-based architectures, multi-modal sensor fusion, lightweight neural networks for real-time deployment, and self-supervised learning techniques. By identifying gaps in current research and outlining potential directions for future work, this survey serves as a valuable reference for researchers and engineers striving to develop robust and adaptive underwater SLAM solutions. Our findings aim to inspire further advancements in autonomous underwater exploration, supporting critical applications in marine science, deep-sea resource management, and environmental conservation.