  We review recent 3D cosmological hydrodynamic simulations of primordial star
formation from cosmological initial conditions (Pop III.1) and from initial
conditions that have been altered by radiative feedback from stellar sources
(Pop III.2). We concentrate on simulations that resolve the formation of the
gravitationally unstable cloud cores in mini-halos over the mass range $10^5 <
M/\Msun < 10^7 $ and follow their evolution to densities of at least $10^{10}
\cmm3$ and length scales of $<10^{-2}$ pc such that accretion rates can be
estimated. The advent of ensembles of such simulations exploring a variety of
conditions permits us to assess the robustness of the standard model for Pop
III.1 star formation and investigate scatter in their formation redshifts and
accretion rates, thereby providing much needed information about the Pop III
IMF. The simulations confirm the prediction that Pop III.1 stars were massive
($\sim 100 \Msun$), and form in isolation in primordial mini-halos. Simulations
of Pop III.2 star forming in relic HII regions suggest somewhat lower masses
($\sim 30 \Msun$) which may help explain the chemical abundances of extremely
metal poor stars. We note that no 3D simulation at present has achieved stellar
density let alone followed the entire accretion history of the star in any
scenario, and thus the IMF of Pop III stars remains poorly determined
theoretically.
