Exploring and monitoring the underwater world using underwater sensors is drawing a lot of attention these days. In this field cooperation between acoustic sensor nodes has been a critical problem due to the challenging features such as acoustic channel failure (sound signal), long propagation delay of acoustic signal, limited bandwidth and loss of connectivity. There are several proposed methods to improve cooperation between the nodes by incorporating information/game theory in the node’s cooperation. However, there is a need to classify the existing works and demonstrate their performance in addressing the cooperation issue. In this paper, we have conducted a review to investigate various factors affecting cooperation in underwater acoustic sensor networks. We study various cooperation techniques used for underwater acoustic sensor networks from different perspectives, with a concentration on communication reliability, energy consumption, and security and present a taxonomy for underwater cooperation. Moreover, we further review how the game theory can be applied to make the nodes cooperate with each other. We further analyze different cooperative game methods, where their performance on different metrics is compared. Finally, open issues and future research direction in underwater acoustic sensor networks are highlighted.