Power line infrastructure is available almost everywhere. Positioning systems aim to estimate where a device or target is. Consequently, there may be an opportunity to use power lines for positioning purposes. This survey article reports the different efforts, working principles, and possibilities for implementing positioning systems relying on power line infrastructure for Power Line Positioning Systems (PLPS). Since Power Line Communication (PLC) systems of different characteristics have been deployed to provide communication services using the existing mains, we also address how PLC systems may be employed to build positioning systems. Although some efforts exist, PLPS are still prospective and thus open to research and development, and we try to indicate the possible directions and potential applications for PLPS.