Undersea acoustic communication (UWAC) is crucial for marine applications such environmental monitoring, defense, and undersea exploration. However, it faces challenges like as multipath propagation, Doppler shifts, absorption losses, and non-stationary channel variations, which impair signal quality and communication reliability. Traditional methods, which usually struggle to adapt to these shifting conditions, are increasingly being replaced by deep learning-based alternatives. This survey investigates the role of Deep Convolutional Autoencoders (DCAEs) and Variational Autoencoders (VAEs) in UWAC. DCAEs enhance channel estimation, noise reduction, and signal reconstruction, whereas VAEs mimic non stationary channels to boost adaptive transmission and forecasting accuracy. Additionally, Autoencoder-based adaptive modulation in conjunction with reinforcement learning dynamically selects the optimal modulation schemes based on SNR and BER constraints to provide dependable communication. Simulation results show that VAE-based models boost channel capacity by up to 52.3% and reduce noise by 73.3% at high SNR levels, while DCAE-based models lower BER by more than 50% when compared to conventional methodologies. These findings show how deep learning-based techniques significantly increase UWAC's flexibility, error resilience, and data rates. Performance metrics, benchmark datasets, and existing models are thoroughly examined, along with remarks about challenges and possible directions for further research. © 2025 Elsevier B.V., All rights reserved.