  It is argued that experimental constraints on theories of asymmetric dark
matter (ADM) almost certainly require that the DM be part of a richer hidden
sector of interacting states of comparable mass or lighter. A general requisite
of models of ADM is that the vast majority of the symmetric component of the DM
number density must be removed in order to explain the observed relationship
$\Omega_B\sim\Omega_{DM}$ via the DM asymmetry. Demanding the efficient
annihilation of the symmetric component leads to a tension with experimental
limits if the annihilation is directly to Standard Model (SM) degrees of
freedom. A comprehensive effective operator analysis of the model independent
constraints on ADM from direct detection experiments and LHC monojet searches
is presented. Notably, the limits obtained essentially exclude models of ADM
with mass 1GeV$\lesssim m_{DM} \lesssim$ 100GeV annihilating to SM quarks via
heavy mediator states. This motivates the study of portal interactions between
the dark and SM sectors mediated by light states. Resonances and threshold
effects involving the new light states are shown to be important for
determining the exclusion limits.
