  The study of protostellar collapse or infall has proven unusually difficult
and controversial. Some historical context will be provided, against which
recent advances can be measured. We now have a substantial number of objects
with signatures that can be interpreted in terms of collapse, but a number of
issues remain. One issue is the effect of chemical variations, especially
depletion in the dense, cold interiors of cores that are likely to form low
mass stars. Strategies for dealing with this issue depend on using dust
emission to constrain the density and temperature distribution, leaving
molecular line observations to constrain dynamics and abundance distributions.
Recent progress in this area will be described and we will consider the next
challenges to be overcome. Interferometeric observations, especially with
future instruments, will provide a powerful tool. In combination with chemical
studies coupled with dynamical models, the observations made possible by
interferometers should finally put this subject on a firm foundation.
