  The event-by-event fluctuations in heavy ion collisions carry information
about the thermodynamic properties of the hadronic system at the time of
freeze-out. By studying these fluctuations as a function of varying control
parameters, such as the collision energy, it is possible to learn much about
the phase diagram of QCD. As a timely example, we stress the methods by which
present experiments at the CERN SPS can locate the second order critical point
at which a line of first order phase transitions ends. Those event-by-event
signatures which are characteristic of freeze-out in the vicinity of the
critical point will exhibit nonmonotonic dependence on control parameters. We
focus on observables constructed from the multiplicity and transverse momenta
of charged pions. We find good agreement between NA49 data and thermodynamic
predictions for the noncritical fluctuations of such observables. We then
analyze the effects due to the critical fluctuations of the sigma field. We
estimate the size of these nonmonotonic effects which appear near the critical
point, including restrictions imposed by finite size and finite time.
