Until quite recently, archaeologists have supposed that the seas and oceans represented a barrier to human dispersal and that islands were among the last places on earth to be colonized by people - only fairly recently - as part of the worldwide spread of modern humans. But is that picture still correct? Startling new data have come to light just in the last few years, in parts of the Mediterranean and in island Southeast Asia, that have been claimed as evidence for a far longer antiquity for seafaring, reaching back hundreds of thousands, and perhaps as much as a million years. Naturally, these claims have attracted widespread attention and much discussion — and not only among archaeologists. This lecture outlines what we know, with reasonable certainty, about patterns of global maritime dispersal in the past few tens of thousands of years, before turning to present the new evidence and its strengths and weaknesses. In trying to understand it, we will need to consider information (amongst other things) from ethnographic analogy, experimental seafaring, and our current knowledge of the relative configurations of land and sea over the course of the Pleistocene era. Some of the bold assertions made in the past few years require more supporting data before they can be accepted. That cautious conclusion does not detract from the excitement and importance of this fast-moving field of research in archaeology.