Complex maritime missions, both above and below the surface, have traditionally been carried out by manned surface ships and submarines equipped with advanced sensor systems. Unmanned Maritime Vehicles (UMVs) are increasingly demonstrating their potential for improving existing naval capabilities due to their rapid deployability, easy scalability, and high reconfigurability, offering a reduction in both operational time and cost. In addition, they mitigate the risk to personnel by leaving the man far-from-the-risk but in-the-loop of decision making. In the long-term, a clear interoperability framework between unmanned systems, human operators, and legacy platforms will be crucial for effective joint operations planning and execution. However, the present multi-vendor multi-protocol solutions in multi-domain UMVs activities are hard to interoperate without common mission control interfaces and communication protocol schemes. Furthermore, the underwater domain presents significant challenges that cannot be satisfied with the solutions developed for terrestrial networks. In this paper, the interoperability topic is discussed blending a review of the technological growth from 2000 onwards with recent authors' in-field experience; finally, important research directions for the future are given. Within the broad framework of interoperability in general, the paper focuses on the aspect of interoperability among UMVs not neglecting the role of the human operator in the loop. The picture emerging from the review demonstrates that interoperability is currently receiving a high level of attention with a great and diverse deal of effort. Besides, the manuscript describes the experience from a sea trial exercise, where interoperability has been demonstrated by integrating heterogeneous autonomous UMVs into the NATO Centre for Maritime Research and Experimentation (CMRE) network, using different robotic middlewares and acoustic modem technologies to implement a multistatic active sonar system. A perspective for the interoperability in marine robotics missions emerges in the paper, through a discussion of current capabilities, in-field experience and future advanced technologies unique to UMVs. Nonetheless, their application spread is slowed down by the lack of human confidence. In fact, an interoperable system-of-systems of autonomous UMVs will require operators involved only at a supervisory level. As trust develops, endorsed by stable and mature interoperability, human monitoring will be diminished to exploit the tremendous potential of fully autonomous UMVs.