They also clean their eyes with their legs. The following video shows a Paddle-tailed Darner (the Happy-face Dragonfly) cleaning its eyes as it rests on its perch. Note the extreme flexibility of the eyes, which can rotate by at least 135˚.
Their eyes are beautiful, almost like small gemstones. Notice that the pseudopupils keep pointing toward the viewer as the head rotates, but that the "eyebrows" move with the eyes themselves. The eyebrows are actually pigment on the surface of the eyes, and are a permanent feature, visible even when the dragonflies dies.