The emergence of commercial underwater acoustic modems from different manufacturers and the promulgation of interoperability standards (e.g., JANUS) broadens the application scenarios of underwater acoustic telemetry and communications. At the same time, security concerns call for authentication and privacy-enforcing schemes. However, compute-or communication-intensive methods for terrestrial networks do not adapt well to bandwidthconstrained acoustic communications. In this context, we discuss the findings of the NATO SPS SAFE-UComm project, which involves research teams from Italy, Israel, Canada, and the UK. The project investigates and realizes practical security schemes that exploit the randomness of physical acoustic communication processes for security, and evaluates the potential of biomimicry and the capability of biomimetic signal detectors. After discussing the concept of SAFE-UComm, we survey its approaches to security through a number of results related to authentication, privacy, and biomimicry functions. Our results, based on several field experiments, show the feasibility of the project's design in relevant scenarios.