  Dark matter self-interactions can affect the small scale structure of the
Universe, reducing the central densities of dwarfs and low surface brightness
galaxies in accord with observations. From a particle physics point of view,
this points toward the existence of a 1-100 MeV particle in the dark sector
that mediates self-interactions. Since mediator particles will generically
couple to the Standard Model, direct detection experiments provide sensitive
probes of self-interacting dark matter. We consider three minimal mechanisms
for coupling the dark and visible sectors: photon kinetic mixing, Z boson mass
mixing, and the Higgs portal. Self-interacting dark matter motivates a new
benchmark paradigm for direct detection via momentum-dependent interactions,
and ton-scale experiments will cover astrophysically motivated parameter
regimes that are unconstrained by current limits. Direct detection is a
complementary avenue to constrain velocity-dependent self-interactions that
evade astrophysical bounds from larger scales, such as those from the Bullet
Cluster.
