As part of the refocusing of NASA from Space Station research to exploration research, we are pursuing a number of proposed and funded projects for lunar exploration using cryogenic techniques. This paper gives a summary of these projects which include: (1) Using passive radiative cooling for separation and storage of volatiles from lunar regolith; (2) Studies of boiling and two-phase flow under lunar gravity; (3) SQUID-based MRI for monitoring astronaut health; (4) Studies of volatiles and water ice in permanently shadowed craters at the lunar poles; and (5) Seismic search for strange quark matter using the Moon as a large and seismically quiet detector.