One of the most basic but intriguing properties of quantum systems is their ability to `tunnel' between configurations which are classically disconnected. That is, processes which are classically impossible, are quantum allowed. In this talk I will outline a new, first-principles approach combining the semiclassical approximation with the concepts of post-selection and weak measurement. Its main virtue is to provide a real-time description within which sharp answers can be given to questions such as 'how long did the tunneling take' and 'where was the particle while it was tunneling?' Potential applications span a vast range, from laboratory tests to understanding black hole evaporation, the stability of the electroweak Higgs vacuum and the future of our universe, and the validity (or otherwise) of the "inflationary multiverse" scenario.