The Planck satellite has measured fluctuations in the Cosmic Microwave Background to high resolution, opening a new window on the early universe. I will show the new cosmological results from Planck, and will summarize the status of current cosmological constraints from the CMB in combination other astrophysical probes. I will discuss the implications for the standard model of cosmology, for inflation in the early universe, and will show constraints on neutrino physics and other extensions to the standard cosmological model.