  We discuss general supersymmetric brane configurations in flux backgrounds of
string and M-theory and derive a necessary condition for the worldvolume theory
to be supersymmetric on a given curved manifold. This condition resembles very
much the conditions found from coupling a supersymmetric field theory to
off-shell supergravity but can be derived in any dimension and for up to
sixteen supercharges. Apart from the topological twist, all couplings appearing
in the supersymmetry condition are linked to fluxes in the bulk. We explicitly
derive the condition for D3-, M2- and M5-branes, in which case the results are
also useful for constructing holographic duals to the corresponding field
theories. In $N=1$ setups we compare the supersymmetry conditions to those that
arise by coupling the field theory to off-shell supergravity. We find that the
couplings of both old and new minimal supergravity are simultaneously realized,
indicating that off-shell supergravity should be coupled via the S-multiplet of
16/16 supergravity in order to describe all supersymmetric brane theories on
curved spaces.
