After the Darkening of Valinor and the destruction of the Two Trees, Telperion the White Tree bore one last Flower of Silver before its end. Aulë and his people made a vessel to carry to the silver flower aloft, and Tilion, one of the hunters of Oromë; was granted the task of steering the new Moon through the sky. Tilion guided his charge up into the western skies just as the Noldor were returning into Middle-earth, and so marked the beginning the First Age. The Moon first rose above Valinor in the far West of the World, but Varda came to change this arrangement, so that the Moon would pass beneath the World, and arise in the east instead, as it does to this day.
According to the legends of the Elves, Tilion was an unsteady steersman, sometimes dwelling overlong beneath the Earth, or appearing in the sky at the same time as the Sun. He was drawn to the bright new Sun, launched from Valinor shortly after his own vessel, and his coming too close to his fiery companion was said to account for the darkening of the Moon's face.
The Moon remained important to the inhabitants of Middle-earth and Númenor throughout their long history. This is perhaps most evident in Elendil's famous son Isildur, whose name means 'Servant of the Moon'. In Middle-earth, he dwelt in Ithilien ('Moon-land') in a tower he named Minas Ithil ('Tower of the Moon'). Though that tower was later captured by the creatures of Sauron, and renamed by Men as Minas Morgul, the symbol of the Moon remained powerful there. Even at the end of the Third Age, its inhabitants still used the Moon as their emblem, though they corrupted that sign with a face of death.
The hobbits had their own tales about the Moon as well, singing songs about a jolly but unpredictable being they named the Man in the Moon. This peculiar figure seems to be an echo of the being described in the Elves' stories, the Maia and hunter Tilion, wayward steersman of the Moon.