Foreseeing the proliferation of underwater vehicles and sensors, underwater wireless optical communication (UWOC) is a key enabler for ocean exploration, with strong competitiveness in short-range bandwidth-intensive applications. We provide a tutorial on the basic concepts and essential features of UWOC, as well as an overview of work being conducted in this field. Research challenges, arising from the characteristics of underwater channels, and possible roadmaps are discussed in detail. This review is expected to be of great use for the link designers of this field.