A system for reverse circulation in a wellbore include equipment for supplying drilling fluid into the wellbore bit via at least an annulus of the wellbore and returning the drilling fluid to a surface location via at least a bore of a wellbore tubular. The system also includes devices for controlling the annulus pressure associated with this reverse circulation. In one embodiment, an active pressure differential device increases the pressure wellbore annulus to at least partially offset a circulating pressure loss. In other embodiments, the system includes devices for decreasing the pressure in the annulus of the wellbore. For offshore application, annulus pressure is decreased to accommodate the pore and fracture pressures of a subsea formation. In still other embodiments, annulus pressure is decreased to cause an underbalanced condition in the well.