Underwater environments have never been much of a constraint to the rich animal life they support at all depths of our seas and oceans. Indeed, nature has taken advantage of this environment to develop a rich variety of efficient communication strategies through evolutionary change and adaptation. The wealth of knowledge to be discovered will continue to dazzle and fascinate the world. For underwater sensor network communication, acoustic signalling is the preferred choice for designers because sound propagation is the most efficient when compared to other forms, like thermal, light, and electromagnetic. It is within this acoustic environment that researchers have to innovate and develop new ideas and methodologies so as to advance the state-of-the-art. In this paper, several fundamental issues and connections are discussed that arise in the study of underwater wireless sensor networks. A variety of ideas and solutions for further research is proposed and fundamental issues in topology control, directional underwater transducers, and monitoring and surveillance are discussed