MEMS (Microelectromechanical System) structures are provided that are designed to rotate in response to thermal actuation or the like. In one embodiment, the MEMS rotary structure includes a hub having one or more radial spoke members that impose a rotational force upon the hub in response to applied changes in temperature. The MEMS rotary structure can also include a ring at least partially encircling the hub and connected to the hub by means of one or more hub spoke members. Controllable clockwise, counterclockwise, or both clockwise and counterclockwise rotation of the hub or ring are provided. The MEMS rotary structures can also include thermal arched beam actuators that are operably connected to the spoke member. As the temperature changes, the thermal arched beam actuators move the spoke members in order to rotate the MEMS structure. Various applications are provided for these rotating MEMS structures, including but not limited to rotary actuators, rotary switches and relays, variable capacitors, variable resistors, shutters, and valves.