The moon is thought to have formed about 4.5 billion years ago, thrown off from the Earth by a collision with another early planetesimal. After this collision it cooled rapidly, with the last of the flood basalts that cover much of the surface of the moon erupting between 3 and 3.5 billion years ago (the most recent major flood basalt eruption on Earth was 65 million years ago, and there is no reason to believe that this will not happen again). Volcanic activity appears to have stopped on the moon about 1.2 billion years ago.
In a paper published in the journal Nature Geoscience on 19 February 2012, a team of scientists led by Thomas Watters of the Center for Earth and Planetary Studies at the Smithsonian Institution describe the discovery of graben -valleys formed by extensional activity - in the Lunar Highlands on the far-side of the moon, by the Lunar Reconnaissance Orbiter Camera, which appear to be less than 50 million years old.
The apparent extensional graben on the moon.
On Earth graben are formed when convection currents in the mantle draw the rocks of the lithosphere apart, causing them to thin, an sag in the middle. In extreme cases these can go on to form new oceans, with spreading centers in the middle forming new crust, though most graben do not progress this far. It is highly unlikely that similar activity is occurring on the moon, but the formation of fresh graben would imply that some sort of geologic activity is happening. Watters et al. suggest the lunar graben may have formed as a result of shrinkage in the lunar crust.
Typical graben formation on Earth. University of Leicester.