Analytic Combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. Primarily due to the efforts of Philippe Flajolet and his many research collaborators, the theory has emerged over recent decades as essential both for the scientific analysis of algorithms in computer science and for the study of scientific models in many other disciplines, including probability theory, statistical physics, computational biology and information theory. This talk surveys thirty years of joint work with Flajolet that was inspired by learning the analysis of algorithms from Knuth and that culminated in the publication of two books: "An Introduction to the Analysis of Algorithms" and "Analytic Combinatorics".