Motivated by forthcoming experiments at RHIC and LHC, we study event-by-eve
nt fluctuations in ultrarelativistic heavy-ion collisions in participant nu
cleon as well as thermal models. The calculated physical observables, inclu
ding multiplicity, kaon to pion ratios, and transverse momenta agree well w
ith recent NA49 data at the SPS, and indicate that such studies do not yet
reveal the presence of new physics. Finally, we present a simple model of h
ow a first order phase transition can be signaled by very large fluctuation
s. (C) 1999 Elsevier Science B.V. All rights reserved.