A double-pole-double-throw (DPDT) electromechanical relay employing a movable first magnet and a nearby third electromagnet is disclosed. The movable first magnet is permanently magnetized with a magnetic moment and has at least a first end and a second end. The third electromagnet, when energized, produces a third magnetic field which is primarily perpendicular to the magnetization direction of the first movable magnet and exerts a magnetic torque on the first magnet to force the first magnet to rotate and closes electrical conduction paths at the first end. Changing the direction of the electrical current in the third electromagnet changes the direction of the third magnetic field and thus the direction of the magnetic torque on the first magnet, and causes the first magnet to rotate in an opposite direction and opens the electrical conduction path at the first end and closes the electrical conduction paths at the second end. Latching, non-latching types, and various forms (normally open or closed, etc.) of relays can be formed by appropriately adjusting various force magnitudes.