Policymakers everywhere are working to determine the set of restrictions that will effectively contain the spread of COVID-19 without excessively stifling economic activity. We show that publicly available data on human mobility-collected by Google, Facebook, and other providers-can be used to evaluate the effectiveness of non-pharmaceutical interventions (NPIs) and forecast the spread of COVID-19. This approach uses simple and transparent statistical models to estimate the effect of NPIs on mobility, and basic machine learning methods to generate 10-day forecasts of COVID-19 cases. An advantage of the approach is that it involves minimal assumptions about disease dynamics, and requires only publicly-available data. We evaluate this approach using local and regional data from China, France, Italy, South Korea, and the United States, as well as national data from 80 countries around the world. We find that NPIs are associated with significant reductions in human mobility, and that changes in mobility can be used to forecast COVID-19 infections.