Liquid 3He and 4He manifest a variety of phenomena at low temperatures. Most prominent among these are the realization of superfluid phases and a number of phase transitions. Some of these transitions can be achieved in an environment that has dimensionality less than three. Further, the ability of mixing the two isotopes yields a rich thermodynamic space that extends in pressure-temperature- concentration, and, in the case of 3He, in magnetic field as well. We have worked on a variety of topics in this field, but, most recently, we have focused on the superfluid transition of 4He in restricted geometries. In these studies, using suitably constructed experimental cells, we can progressively eliminate one spacial variable at a time. This results in "films," "channels," and "boxes." Phase transitions in any system are strongly modified in these limits. This can be calculated theoretically. For many reasons, superfluid 4He is ideally suited for these studies and can be used as a critical test of the theoretical calculations. Our research has been funded by the National Science Foundation since 1976.