This book presents numerical differential quadrature (DQ) - based methods recently developed by the author. Their ability for solving generic scientific and engineering problems is demonstrated. These methods are the generic differential quadrature, the extended differential quadrature and the related discrete element analysis methods. These novel numerical techniques are both efficient and reliable. They are suitable for developing solution algorithms for various computational mechanics problems with arbitrarily complex geometry. This is shown for several comprehensive examples such as bars and beams, trusses, frames, general field problems, elasticity problems or bending of plates.