Observations of the low solar corona in the extreme ultraviolet and in soft X-rays evidence a close relationship of coronal dimmings and coronal mass ejections (CMEs). Dimmings are usually interpreted as places of plasma evacuation during a CME. We characterize a CME by the apparent angular extent of associated dimmings above the solar limb and define a global CME as a CME with the total apparent extent of limb dimmings of more than 180°. Several examples of global CMEs are discussed. All the global CMEs identified up to now are fast full-halo CMEs associated with X-class flares (if they originate on the front side of the Sun). We demonstrate that global CMEs involve an eruption of several magnetic flux systems distributed on a large spatial scale comparable to one-half of the solar disk (true angular width around 180°). We discuss possible interpretations of the global CME phenomenon and challenges it presents to CME modeling. Our results suggest a nonlocal nature of the CME eruption mechanism.