Plavy was first mentioned in 1644. The name of the village was probably derived from floating (plavení) of timber or ore mined in the surroundings. The first residents of the village were woodcutters, charcoal burners and metalworkers mining ore.

Near the village, a few kilometres to the south, there is Bozkovské jeskyně. Lovers of winter sports may visit nearby Krkonoše or Jizerské hory offering plenty of tended cross-country ski tracks or downhill slopes.