The origin of ice slipperiness has been a matter of great controversy for more than a century, but an atomistic understanding of ice friction is still lacking. Here, we perform computer simulations of an atomically smooth substrate sliding on ice. In a large temperature range between 230 and 266 K, hydrophobic sliders exhibit a premelting layer similar to that found at the ice/air interface. On the contrary, hydrophilic sliders show larger premelting and a strong increase of the first adsorption layer. The nonequilibrium simulations show that premelting films of barely one-nanometer thickness are sufficient to provide a lubricating quasi-liquid layer with rheological properties similar to bulk undercooled water. Upon shearing, the films display a pattern consistent with lubricating Couette flow, but the boundary conditions at the wall vary strongly with the substrate's interactions. Hydrophobic walls exhibit large slip, while hydrophilic walls obey stick boundary conditions with small negative slip. By compressing ice above atmospheric pressure, the lubricating layer grows continuously, and the rheological properties approach bulk-like behavior. Below 260 K, the equilibrium premelting films decrease significantly. However, a very large slip persists on the hydrophobic walls, while the increased friction on hydrophilic walls is sufficient to melt ice and create a lubrication layer in a few nanoseconds. Our results show that the atomic-scale frictional behavior of ice is a combination of spontaneous premelting, pressure melting, and frictional heating.