This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, differential quadrature, residual distribution, spectral volume, spectral difference, flux reconstruction, and lifting collocation penalty methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an undergraduate of the state-of-the-art and remaining challenges in high-order CFD methods.