UASNs are widely used in many applications, and many studies have been conducted. However, most current research projects have not taken network security into consideration, despite the fact that a UASN is typically vulnerable to malicious attacks due to the unique characteristics of an underwater acoustic communication channel (e.g., low communication bandwidth, long propagation delays, and high bit error rates). In addition, the significant differences between UASNs and terrestrial wireless sensor networks entail the urgent and rapid development of secure communication mechanisms for underwater sensor nodes. For the above mentioned reasons, this article aims to present a somewhat comprehensive survey of the emerging topics arising from secure communications in UASNs, which naturally lead to a great number of open research issues outlined afterward.