SummaryUnderwater acoustic channel is a challenging medium for communication due to the presence of significant multipath, high noise, frequency‐dependent propagation loss, and high and non‐uniform Doppler spread. Doppler shift is non‐negligible in underwater communication due to the low velocity of underwater signals. Synchronization and Doppler estimation are important requirements for achieving good performance in this channel. Synchronization algorithms that give good performance in radio communication do not work well in underwater communication. Hence, this area has received a lot of attention from researchers. This paper surveys important works in the area. The techniques proposed in the literature for frame synchronization, frequency and phase synchronization, and timing synchronization in single carrier communications are reviewed here. The synchronization techniques proposed for OFDM, MIMO OFDM, and spread spectrum communication are also surveyed. Doppler estimation methods proposed in the literature are also reviewed. It is found that most of the recent works in underwater acoustic communication focus on OFDM synchronization. Deep learning‐based methods proposed in the literature are also reviewed. Key open problems and areas that require future research attention in the field of synchronization and Doppler estimation in underwater communications are highlighted in this paper. The area needing most attention of underwater communication researchers was found to be MIMO OFDM due to the difficulty in synchronization in such systems while used in underwater communication. Reducing the computational complexity of the algorithms used is also important for future work. Schemes that work with Doppler due to relative velocity over 10 m/s also need to be developed.