A switchable wire includes filaments, each of which includes a heat-activated material layer that may be indirectly heated to change its state between different states having different electrical conductivity. In an example embodiment the indirect heating may be electrically resistance heating by passing electrical current through an electrically-resistive core of the filament. The heat passing through an electrically-insulative coating around the core, and into a heat-activated material layer around the electrically-insulative coating. The heat-activated material may be a chalcogenide material that is shiftable between a crystalline electrically-conducting state and an amorphous electrically-insulating state. The state of the material may be controlled by controlling the heating profile through controlling heating in the core. Many such filaments may be twisted together to form a switchable wire. Such wires may be used in any of a variety of devices where switchable electrical conductivity is desired.