A dark matter that interacts with itself as strongly as Standard Model particles interact with each other via the strong force is allowed by current observational constraints. Dark matter self-interactions in this magnitude are a possible solution to the biggest remaining problem in our current cosmological standard model (LCDM), the cusp/core problem.I will review what are the current astrophysical constraints on the dark matter self-interaction cross section coming from simulations and observations of galaxy clusters, low mass spirals and Milky Way dwarf spheroidal galaxies. Then I will talk about how we can tighten these constraints or even yield a measure on the dark matter self-interaction cross section through a comprehensive program of simulations and observations of merging galaxy clusters.