  We construct three classes of generalised orbifolds of Reshetikhin-Turaev
theory for a modular tensor category $\mathcal{C}$, using the language of
defect TQFT from [arXiv:1705.06085]: (i) spherical fusion categories give
orbifolds for the "trivial" defect TQFT associated to vect, (ii) $G$-crossed
extensions of $\mathcal{C}$ give group orbifolds for any finite group $G$, and
(iii) we construct orbifolds from commutative $\Delta$-separable symmetric
Frobenius algebras in $\mathcal{C}$. We also explain how the Turaev-Viro state
sum construction fits into our framework by proving that it is isomorphic to
the orbifold of case (i). Moreover, we treat the cases (ii) and (iii) in the
more general setting of ribbon tensor categories. For case (ii) we show how
Morita equivalence leads to isomorphic orbifolds, and we discuss
Tambara-Yamagami categories as particular examples.
