A microsystem switch (1, 20, 25, 30, 33) has a support (2) defining a recess (3), and a flexible bridge (6) is mounted on the support (2) bridging the recess (3). The bridge (6) is shaped so as to hold selectively a concave stable state, in which the bridge bulges into the recess (3), and a convex stable state in which the bridge bulges out of the recess (3). The switch includes an actuator (8, 9; 26, 27) for effecting flexing of the bridge (6) between the stable states, and a switching element (7, 31, 34) is mounted on the bridge (6) such that movement of the bridge between the stable states moves the switching element between an on position and an off position. According to another design, a microsystem switch (40, 55) has a support (41) defining a recess (42), and an elongate torsion member (44) is mounted on the support (41) bridging the recess (42). A flexible bridge (43, 56) is mounted on the support (41) bridging the recess (42) in a direction substantially perpendicular to the torsion member (44). The bridge (43, 56) is connected to the torsion member (44) at the cross-point thereof so that a first section of the bridge extends between the cross-point and one side of the recess (42) and a second section of the bridge extends between the cross-point and the opposite side of the recess (42). The bridge (43, 56) is shaped so as to hold selectively a first stable state, in which the first section of the bridge bulges into the recess and the second section of the bridge bulges out of the recess, and a second stable state in which this configuration is reversed. A switching element (45) is mounted at the cross-point of the bridge (43, 56) and torsion member (44), and an actuator (46a, 46b; 58a, 58b) is again provided for effecting flexing of the bridge (43, 56) between the stable states. Here, movement of the bridge (43, 56) between the stable states effects twisting of the torsion member (44) and rotation of the switching element (45) between an on position and an off position. Switching devices incorporating these switches, and switching apparatus comprising arrays of such switching devices, are also provided.