  This is an invited contribution to the 2nd edition of the Encyclopedia of
Mathematical Physics. We give an overview of 3-dimensional topological quantum
field theories (TQFTs) and the corresponding quantum invariants of 3-manifolds.
We recall the main algebraic concepts and constructions, such as modular and
spherical fusion categories, the Witten-Reshetikhin-Turaev and Turaev-Viro
theories, and the relation between these two TQFTs. We also briefly discuss
generalizations of these constructions by providing a (non-exhaustive) review
of some recent works on 3-dimensional extended TQFTs, defect TQFTs, homotopy
QFTs, and non-semisimple TQFTs.
