The phenomenological constraints on extra neutral gauge bosons at present a
nd at future colliders are reviewed. Special attention is paid to the influ
ence of radiative corrections, systematic errors, and kinematic cuts on the
Z' constraints. Simple estimates of the Z' constraints from different reac
tions are derived. They make the physical origin of these constraints trans
parent. The results existing in the literature are summarized and compared
with the estimates. The consequence of model assumptions on the Z' constrai
nts is discussed. The paper starts with an overview of Z' parameters and th
e possible links between them by model assumptions. It continues with a dis
cussion of Z' limits and Z' measurements in different reactions at e(+)e(-)
and mu(+)mu(-) colliders. It follows an overview of the corresponding limi
ts at proton colliders. Possible Z' constraints from other reactions as ep
collisions, atomic parity violation, neutrino scattering and cosmology are
briefly mentioned. (C) 1999 Elsevier Science B.V. All rights reserved.