This book examines Saul Kripke's influential interpretation of the later Wittgenstein, as presented in Wittgenstein on Rules and Private Language (1982), alongside the principal objections raised by over twenty philosophers. After introducing the foundational notions underlying Kripke's sceptical challenge, the book analyses different aspects of the 'sceptical argument' Kripke attributes to Wittgenstein and explicates the 'sceptical solution' he takes Wittgenstein to offer as an alternative to classical realism. It further investigates how the sceptical problem, as well as an additional, special problem, arises in the attribution of sensations and in traditional approaches to the problem of other minds. The final sections focus on the major responses to Kripke's reading from prominent philosophers engaged with the topic since the 1980s, including John McDowell, Simon Blackburn, Gordon Baker, Peter Hacker, Colin McGinn, Crispin Wright, Paul Boghossian, Philip Pettit, Barry Stroud, Hannah Ginsborg, Alexander Miller, George Wilson, Scott Soames, Noam Chomsky, Paul Horwich, as well as Norman Malcolm, Donald Davidson, David Lewis, Christopher Peacocke, Jerry Fodor, David Stern, Alex Byrne, Ruth Millikan, Hilary Putnam and John Searle.