Diffeomorphism groups of compact manifolds and their subgroups are prime examples of infinite dimensional Lie groups. The present thesis generalizes the results on diffeomorphism groups of manifolds to diffeomorphism groups of orbifolds. One might think of an orbifold as a manifold with "mild singularities". Objects with orbifold structure arise naturally, for example in symplectic geometry, physics and algebraic geometry. The main result of the thesis is the construction of a Lie group structure for diffeomorphism groups of reduced paracompact orbifolds. Furthermore, we give an explicit description of the Lie algebra associated to the diffeomorphism group. Moreover, we show that for sigma-compact orbifolds the Lie groups constructed are (strongly) C^0-regular. In particular this implies regularity in the sense of Milnor. To obtain these results, we need auxiliary results from the theory of orbifolds and their morphisms. Our goal is to present a mostly self contained exposition of this theory.