  A concise, somewhat personal, review of the problem of superfluidity and
quantum criticality in regular and disordered interacting Bose systems is
given, concentrating on general features and important symmetries that are
exhibited in different parts of the phase diagram, and that govern the
different possible types of critical behavior. A number of exact results for
various insulating phase boundaries, which may be used to constrain the results
of numerical simulations, can be derived using large rare region type
arguments. The nature of the insulator-superfluid transition is explored
through general scaling arguments, exact model calculations in one dimension,
numerical results in two dimensions, and approximate renormalization group
results in higher dimensions. Experiments on He-4 adsorbed in porous Vycor
glass, on thin film superconductors, and magnetically trapped atomic vapors in
a periodic optical potential, are used to illustrate many of the concepts.
