What can we never do? Barrow looks at what limits there might be to human discovery, and what we might find, ultimately, to be unknowable, undoable, or unthinkable. Science is a big success story, but where will it end? And, indeed, will it end? Weaving together a tapestry of surprises, Barrow explores the frontiers of knowledge. We find that the notion of 'impossibility' has played a striking role in our thinking. Surrealism, impossible figures, time travel, paradoxes of logic and perspectives - all stimulate us to contemplate something more than what is. Using simple explanations, it shows the reader that impossibility is a deep and powerful notion; that any Universe complex enough to contain conscious beings will contain limits on what those beings can know about their Universe; that what we cannot know defines reality as surely as what we can know.