**Algorithmic quantum simulation**

The concept of quantum computing developed from the desire to simulate quantum systems efficiently, and this original motivation now motivates much experimental quantum computing research because the resource requirements are conceivably within reach. I begin with an historical background to quantum simulation including exegesis of Feynman's seminal 1982 paper on quantum computing and then explain how efficient algorithms are constructed for simulating quite general quantum dynamics. Finally I discuss outcomes of efficient quantum simulation such as answering many-body physics problems and constructing a linear equation solver.