The feasibility of magnetohydrodynamic (MHD) ship propulsion using superconducting magnets is reviewed in light of recent advances in high-temperature superconductivity. The scaling relations for the electrical and hydraulic efficiencies of MHD pump-jets show that overall efficiencies >50% are feasible at speeds of 40 knots and higher provided that magnetic fields >5T can be maintained over volumes of the order of 100 m3. The development of large-scale electrical machinery and magnets using the high-temperature superconductors now under development could make it practical to construct submersibles for high-speed and silent operation. Low-speed tankers for movement of bulk cargo would be efficient with even lower fields.