Black holes, dark matter and dark energy are the most important constituents of the Universe, but don't emit light and are therefore invisible. Prof. Longair describes why we are confident that all three exist, amidst illustrations of recent results from a wide range of ground-based and space telescopes, simulations and movies. The talk is delivered at a non-technical level and suitable for young people. Prof. Malcolm Longair CBE has been Astronomer Royal for Scotland, director of the Royal Observatory Edinburgh, and president of the Royal Astronomical Society. His award-winning research has led to 8 books, and he is perhaps most widely known for delivering the RI Christmas lectures. This lecture was delivered at the Edinburgh Filmhouse, 22nd July 2010.