  There is strong evidence in favor of the idea that dark matter is self
interacting, with the cross section-to-mass ratio $\sigma / m \sim
1\,\mathrm{cm^2/g} \sim 1\,\mathrm{barn/GeV}$. We show that viable models of
dark matter with this large cross section are straightforwardly realized with
non-Abelian hidden sectors. In the simplest of such models, the hidden sector
is a pure gauge theory, and the dark matter is composed of hidden glueballs
with a mass around $100\,\mathrm{MeV}$. Alternatively, the hidden sector may be
a supersymmetric pure gauge theory with a $\sim 10\,\mathrm{TeV}$ gluino
thermal relic. In this case, the dark matter is largely composed of
glueballinos that strongly self interact through the exchange of light
glueballs. We present a unified framework that realizes both of these
possibilities in anomaly-mediated supersymmetry breaking, where, depending on a
few model parameters, the dark matter may be composed of hidden glueballinos,
hidden glueballs, or a mixture of the two. These models provide simple examples
of multicomponent dark matter, have interesting implications for particle
physics and cosmology, and include cases where a subdominant component of dark
matter may be extremely strongly self interacting, with interesting
astrophysical consequences.
