We think the moon formed when a Mars-sized planet (Theia) smashed into the proto-Earth four and a half billion years ago. This remarkable idea is supported by the geology of moon rocks, brought back by the Apollo astronauts between 1968-1974, and by much more recent computer simulations.
But one puzzle remains: the relative proportions of oxygen isotopes are identical for Earth rocks and moon rocks. (Isotopes are different forms of an element that vary only in the mass of their atoms.) Originally this was taken to mean that the moon and Earth came from the same source — neatly supporting the impact hypothesis — until the computer simulations showed that most of the moon must be derived from Theia, not Earth. But Theia must have had a different proportion of oxygen isotopes to the proto-Earth.
This paradox is resolved by recent calculations. These show that the collision between Theia and proto-Earth was so violent that both bodies were extensively melted or vaporized and thoroughly mixed before Earth and moon condensed after just 1000 years. This eliminated variations in the proportions of oxygen isotopes.
This is exciting research as it implies that moon rocks may resemble the rocks of early Earth. Ironically we can't find rocks from Earth's earliest times here because plate tectonics and weathering has destroyed such ancient material. It seems that to learn about early Earth we should look to the moon.