There is strong evidence in favor of the idea that dark matter is self interacting, with the cross section-to-mass ratio $\sigma /m\sim 1{\mathrm{cm}}^2/\mathrm{g}\sim 1\mathrm{barn}/\mathrm{GeV}$. 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 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.

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