  We derive the transverse projection operators for fields with arbitrary
integer and half-integer spin on three-dimensional anti-de Sitter space,
AdS$_3$. The projectors are constructed in terms of the quadratic Casimir
operators of the isometry group $\mathsf{SO}(2,2)$ of AdS$_3$. Their poles are
demonstrated to correspond to (partially) massless fields. As an application,
we make use of the projectors to recast the conformal and topologically massive
higher-spin actions in AdS$_3$ into a manifestly gauge-invariant and factorised
form. We also propose operators which isolate the component of a field that is
transverse and carries a definite helicity. Such fields correspond to an
irreducible representation of $\mathsf{SO}(2,2)$. Our results are then extended
to the case of $\mathcal{N}=1$ AdS$_3$ supersymmetry.
