This is a joint PACM/ORFE Colloquium:  We describe a framework for exact post-selection inference.At the core of our framework is what we call selective inferencewhich allows us to define selective Type I and II errors for hypothesis tests and selective coverage for intervals.  Several examples are discussed including the LASSO, forward stepwise, change point detection.  This is joint work with several: Will Fithian, Jason Lee, Richard Lockart, Joshua Loftus, Dennis Sun, Yuekai Sun, Ryan Tibshirani, Rob Tibshirani.