I will review the latest results on cosmic microwave background (CMB) anisotropies measured by the Planck satellite. These measurements agree extremely well with a spatially flat, cosmological constant dominated cosmology with nearly scale invariant Gaussian fluctuations, as predicted by inflationary models of the early Universe. However, there are some discrepancies with other astrophysical measurements, most notably with direct measurements of the Hubble constant. The Planck measurements also show the emergence of a hierarchy in the parameters defining inflationary models. Should we worry about these results? I will argue that these peculiarities may be pointers to new physics.