The Anthropocene is a geological epoch marked by major human influences on processes in the atmosphere, biosphere, hydrosphere and geosphere. One of the most dramatic features of the Anthropocene is the massive alteration of the Earth's vegetation, including forests. Here we investigate the role of topography in shaping human impacts on tree cover from local to global scales. We show that human impacts have resulted in a global tendency for tree cover to be constrained to sloped terrain and losses to be concentrated on flat terrain. This effect increases in strength with increasing human pressure and is most pronounced in countries with rapidly growing economies, limited human population stress and highly effective governments. These patterns likely reflect the relative inaccessibility of sloped topography and have important implications for conservation and modelling of future tree cover.