NASA’s New Horizons spacecraft has revealed the complex geology of Pluto and Charon. Pluto’s encounter hemisphere shows ongoing surface geological activity centered on a vast basin containing a thick layer of volatile ices that appears to be involved in convection and advection, with a crater retention age no greater than ~10 million years. Surrounding terrains show active glacial flow, apparent transport and rotation of large buoyant water-ice crustal blocks, and pitting, the latter likely caused by sublimation erosion and/or collapse. More enigmatic features include tall mounds with central depressions that are conceivably cryovolcanic and ridges with complex bladed textures. Pluto also has ancient cratered terrains up to ~4 billion years old that are extensionally faulted and extensively mantled and perhaps eroded by glacial or other processes. Charon does not appear to be currently active, but experienced major extensional tectonism and resurfacing (probably cryovolcanic) nearly 4 billion years ago. Impact crater populations on Pluto and Charon are not consistent with the steepest impactor size-frequency distributions proposed for the Kuiper belt.