Abstract: The standard cosmological model with collisionless, cold dark matter (CDM) is remarkably successful in describing the observed large-scale structure of the Universe; however, on small scales ranging from dwarf spheroidal galaxies to galaxy clusters, dark matter halos have more cored profiles with lower central densities than those generated by simulations. An attractive solution to these anomalies is to modify predictions of small-scale structure through dark matter self-interactions. I will discuss a particular model in which dark matter is the analog of hydrogen in a secluded sector. The self-interactions, which include both elastic scatterings as well as inelastic processes due to a hyperfine transition, exhibit the right velocity dependence to explain the low dark matter density cores seen in spiral galaxies while being consistent with all constraints from observations of clusters of galaxies. Significant cooling losses may occur due to excitations and subsequent decays of the hyperfine state, which may affect the evolution of low-mass halos and the early growth of black holes. Furthermore, the interaction between dark matter and dark radiation suppresses the matter power spectrum at small scales, resulting in minimum halo masses that are significantly larger than those typically predicted by CDM.