Opening the window on strongly interacting dark matter

We discuss the possibility that the dark matter consists of strongly interacting massive particles (SIMP's) which have cross sections with ordinary matter which are larger than characteristic weak-interaction cross sections. We show that, while results from decay, cosmic-ray detectors, galactic-halo stability, the cooling of molecular clouds, proton-decay detectors, and the existence of old neutron stars and the Earth constrain the interactions of the missing matter with ordinary matter over a broad range of parameter space, there still exist several windows for SIMP's. It is noteworthy that there are two regions of less than geometric cross sections: one with masses of 10^5-10^7 GeV and another with masses above 10^10 GeV.