From the standpoint of mechanics all moving objects, like machines and mechanisms in engineering or animals in biology, are characterized by the kinematics and kinetics of the movable rigid or elastic bodies and by certain constraints, which might be bilateral or unilateral. A complete set of constraints may be interpreted as an abstract mapping of a machine, because constraints are responsible for the functional realization of the designed machine motion. Classical multibody theory includes bilateral constraints. Only recently has multibody theory been extended to unilateral constraints. The consideration of multiple contact processes was outside the domain of solution possibility in the past. Since then potential applications have exploded. This paper gives a survey of these applications.