With the advances in technology, there has been an increasing interest from researchers and industrial institutions in the use of underwater wireless sensor networks (UWSNs). Constrained by the open acoustic channel, harsh underwater environment, and their own particularities, UWSNs are vulnerable to a wide class of security threats and malicious attacks. However, most existing research into UWSNs has not taken security into consideration. Moreover, the existing relatively mature security mechanisms for WSNs cannot be directly utilized in UWSNs. For these reasons, this article aims to present a comprehensive overview of the particularities, constraints, attacks, challenges and current security mechanisms of UWSNs. In addition, challenging, open and hot research topics are outlined.