A stable sexaquark (S) composed of uuddss is a compelling Dark Matter candidate and would not have been discovered in accelerator experiments to date. I will briefly review its particle properties, why the S would have eluded searches for an H-dibaryon, and analyses of Upsilon decay and LHC data suitable to discovering it (as are now underway by BABAR, Belle, CMS and LHCb). The main focus of the talk will be direct detection constraints on S Dark Matter, and two major almost model-independent cosmological consequences: predicted Omega_DM/Omega_b = 4.5-6, in excellent agreement with the 5.3 +- 0.1 observed, and 7Li abundance in agreement with observation (which is ~10sigma below the standard LCDM prediction). The Omega_DM/Omega_b prediction follows from statistical physics at the QGP-hadronization transition and approximately applies also for strange quark nuggets, but the 7Li result requires sexaquark DM. For the relevant parameter space of S interactions with nucleons via omega-phi and f0 meson exchange, Born Approximation does not apply, requiring a complete re-evaluation of Direct Detection experiments, as will be reported. Time permitting, new direct detection limits for generic hadronically interacting Dark Matter forming an atmosphere within and around Earth will be given, and additional astrophysical consequences of HIDM will be discussed.