Nearly everyone agrees they must be the result of some weird space-weather process. Because the moon does not have a global magnetic field like Earth does, the lunar surface is bombarded by the solar wind - a constant flow of charged particles coming from the sun.
This "space weathering" darkens and reddens the powdery regolith exposed on the surface. For example, fresh lunar craters - like the gigantic Tycho impact crater visible to the naked eye - are easy to find because the ejecta are comparatively young and bright because they haven't had time to darken.
Lunar probes have found that the swirl regions have a peculiar localized magnetic field. Two Apollo missions left behind so-called "subsatellites" that flew just 60 miles above the lunar terrain. Scientists discovered that the satellites passed in and out of magnetic regions sprouting out of the lunar surface. The moon has a crazy quilt of magnetic patches, much as Mars does.
A localized magnetic field could shield Reiner Gamma from the solar wind, reducing space weathering and preserving the relative "young"-looking brightness of swirls relative to darker surround terrain. This means lunar swirls are merely a shadow of the magnetic forces arching above them.
But how did it happen?
A nagging puzzle is that swirls like these are not found on any other planetary body we have viewed close-up. This is especially true for moon-like Mercury, which is being closely photographed by NASA's MESSENGER orbiter.
This would rule out the hypothesis that the swirls were caused by comets hitting the moon. Some scientists have proposed that the coma of a comet streaking in just above the moon would change the surface properties. Or perhaps falling fragments from a comet nucleus broken up by gravitational tidal forces ploughed into the regolith, imprinting a pattern. But comets should have hit Mercury too.
It also challenges another hypothesis - that lunar swirls on the moon's farside at Mare Ingenii and Mare Marginis are somehow associated with large impact structures on the exactly opposite side if the moon - Mare Imbrium and Mare Orientale.
The idea is that 4 billion years ago an asteroid impact sent a super-hot plasma wave sweeping around the moon and ploughing a primeval global magnetic field in front of it. The plasma cloud would converge at a point directly opposite the impact, concentrating the magnetic field at that point. Over billions of years the moon's core cooled and its global magnetic field faded away, leaving behind forensic evidence in tangled magnetic patches - the swirls. Again, similar impact events happened on Mercury, but no swirls resulted.
This leaves behind the puzzle that the moon simply has localized crustal magnetic anomalies for no obvious reason. Science fiction fans will remember that the iconic alien monolith in the 1968 film "2001: A Space Odyssey" was called TMA-1 (Tycho Magnetic Anomaly One) because it was detected as an intense magnetic field inside the crater Tycho.
The Reiner Gamma formation would be a fascinating site for future human exploration. They wouldn't find a monolith, but if astronauts brought along a magnetic compass the needle would wildly swing back and forth. And, the localized field would helpfully shield them from the solar wind.