The gas-kinetic methods for viscous flow simulations have attracted much attention and become mature during the past decade. Ever since they were originally invented for compressible gas flows, the gas-kinetic methods have been extended to various viscous flow problems with a large number of applications. This book not only provides an introduction to the gas-kinetic methods, but also presents some recent progress on these useful and powerful methods. Besides the original gas-kinetic finite volume scheme for the Euler and Navier-Stokes equations, the book also covers in detail the following extensions of the method: the high order gas-kinetic Runge-Kutta discontinuous Galerkin finite element method for Navier-Stokes equations, the multiscale gas-kinetic method for flows in near continuum regime including rarefied gas and microscale gas flows, the multiple temperature kinetic model for microscale flow problems. Plenty of numerical examples are exhibited to validate these methods. The book addresses researchers as well as graduate students and engineers interested in learning, using, or further developing the gas- kinetic methods.