The radii and masses of dark matter halos are an essential input for models of galaxy formation, and for the interpretation of numerous observations. These radii are typically defined through an arbitrary overdensity threshold, largely because the density profiles of halos are thought not to have a well-defined edge. In this talk, I will show that the situation is more complicated: the outer profiles of halos depend on their dynamical state, and exhibit a novel feature called the splashback radius. I will argue for this radius as a physically motivated halo boundary and discuss recent observational and theoretical results supporting this notion. I will introduce a new analysis code that tracks billions of particle orbits in cosmological simulations in unprecedented detail. Based on the resulting measurements, I will demonstrate that the splashback radius contains complex information about halos that cannot be derived from conventional radius definitions.