Vacuumed gap membrane distillation (VAGMED) modules, and multi-stage VAGMED systems and processes using the modules are provided. In an embodiment, the membrane distillation modules (10) can comprise: a) a condenser (12) including a condensation surface (15); b) a first passageway (13) having an inlet for receiving a first feed stream (14) and an outlet through which the first stream can pass out of the first passageway, the first passageway configured to bring the first feed stream into thermal communication with the condensation surface; c) an evaporator (17) including a permeable evaporation surface allowing condensable gas to pass there through; d) a second passageway (18) having an inlet for receiving a second feed stream (19) and an outlet through which the second feed stream can pass out of the second passageway, the second passageway configured to bring the second feed stream into communication with the permeable evaporation surface; and e) an enclosure (24) providing a vacuum compartment within which the condenser, the evaporator and the first and second passageways of the module are contained.