We develop a general theory of 1-, 2-, and 3-dimensional "orbifold completion", to describe (generalised) orbifolds of topological quantum field theories as well as all their defects. This can be viewed as the "oriented version" of condensation completion. We give a basic introduction to TQFTs and their orbifolds, and discuss applications which include defect TQFTs for state sum models, Reshethikin-Turaev and Crane-Yetter theory. This is joint work with Lukas Müller.