Quantum physics is one of the most successful branches of science. Its conceptual foundations, however, are replete with-paradoxes, and the implications of the theory for the nature of reality are profound. Interest in this topic has been re-awakened by a key experiment performed in 1982 to test the foundations of the theory. The occasion prompted BBC Radio to make a documentary (of the same title as the book) on the conceptual foundations of quantum mechanics, for Radio 3. This book is based on the original transcripts of this broadcast, including interviews with several physicists who have played a prominent part in the debate on these paradoxes. The book also contains an introduction to quantum physics, its puzzles and paradoxes, and the contending proposed resolutions thereof, written at a non-specialist level. There is also a glossary and a bibliography.