Multibody dynamics is based on analytical mechanics and is applied to engineering systems such as a wide variety of machines and all kind of vehicles. Multibody dynamics depends on computational dynamics and is closely related to control design and vibration theory. Recent developments in multibody dynamics focus on elastic or flexible systems, respectively, contact and impact problems, and actively controlled systems. Some fundamentals in multibody dynamics, recursive algorithms and methods for dynamical analysis are presented. In particular, methods from linear system analysis and nonlinear dynamics approaches are discussed. Also, applications from vehicles, manufacturing science and molecular dynamics are shown.