I present the results of ultra-high resolution simulations of the formation and evolution of primordial proto-stellar clouds. The calculations include optically thick line cooling and collision-induced emission, as well as complete chemistry network of primordial gas at high densities, and hence can follow the cloud evolution to densities beyond 1015 per cc. The gas cloud does not fragment, although chemo-thermal instability occurs. I explain why. The final mass accretion rate is found to be very large, and the central cloud has a small angular mometum. I discuss the implications. Preliminary results from simulations of early HII/HeIII regions are also presented.