In this talk I will present an overview of recent simulations of Population III star formation in a cosmological context. Recent published and unpublished work by multiple groups of authors using fundamentally different computational methods appears to have converged to give a consistent view of Population III star formation. In the absence of a photodissociating background, Population III protostellar cores form within small (5x10⁵ - 10⁶ solar mass) cosmological halos. Due to the relatively poor cooling properties of molecular hydrogen, collapse of the halo core occurs quasistatically until high densities (on the order of 10⁸ cm^-3) are reached, at which point 3-body molecular hydrogen formation takes place and the collapse accelerates. The collapsing core finally forms a hydrostatic protostar with mass of ~0.001 Msun. At this point, cosmological simulations do not have sufficient physics to continue the calculations (and to determine the Population III IMF) and different methods must be considered.