  History, status and plans of the search for critical behavior of strongly
interacting matter created in nucleus-nucleus collisions at the CERN Super
Proton Synchrotron is reviewed. In particular, it is expected that the search
should answer the question whether the critical point of strongly interacting
matter exists and, if it does, where it is located.
  First, the search strategies are presented and a short introduction is given
to expected fluctuation signals and to the quantities used by experiments to
detect th The most important background effects are also discussed.
  Second, relevant experimental results are summarized and discussed. It is
intriguing that both the fluctuations of quantities integrated over the full
experimental acceptance (event multiplicity and transverse momentum) as well as
the bin size dependence of the second factorial moment of pion and proton
multiplicities in medium-sized Si+Si collisions at 158A GeV/c suggest critical
behaviour of the created matter.
  These results provide strong motivation for the ongoing systematic scan of
the phase diagram by the NA61/SHINE experiment at the SPS and the continuing
search at the Brookhaven Relativistic Hadron Collider.
