Recent work which has significantly honed the geometric understanding
and interpretation of the moduli space of certain N = 2 superconformal
field theories is reviewed. This has resolved some important issues i
n mirror symmetry and has also established that string theory admits p
hysically smooth processes which can result in a change in topology of
the spatial universe. Recent work which illuminates some properties o
f physically related theories associated with singular spaces such as
orbifolds is described.