Global simulations are a powerful tool to study the Earth’s magnetosphere and its interaction with the solar wind, as they provide the global view lacking in localized spacecraft observations. A large number of global simulations of near-Earth space are based on magnetohydrodynamics, describing processes occurring at large scales. In the recent years, the increase in available computational power has made it possible to develop global kinetic simulations, thus including small-scale processes in a global context. The Vlasiator code, currently developed at the University of Helsinki, uses a so-called hybrid-Vlasov approach and provides simulations of the Earth’s magnetosphere in its real physical scales while including ion kinetic effects. In this talk, I will review some of the recent results obtained with the Vlasiator code, both in the dayside and the nightside magnetosphere, concerning magnetopause and tail reconnection, particle acceleration, and foreshock processes. I will in particular emphasize the connections between large- and small-scale phenomena and between the different regions of geospace, which can readily be studied in global kinetic simulations.