  We review current ideas on entropy production during the different stages of
a relativistic nuclear collision. This includes recent results on decoherence
entropy and the entropy produced during the hydrodynamic phase by viscous
effects. We start by a discussion of decoherence caused by gluon bremsstrahlung
in the very first interactions of gluons from the colliding nuclei. We then
present a general framework, based on the Husimi distribution function, for the
calculation of entropy growth in quantum field theories, which is applicable to
the early ("glasma") phase of the collision during which most of the entropy is
generated. The entropy calculated from the Husimi distribution exhibits linear
growth when the quantum field contains unstable modes and the growth rateis
asymptotically equal to the Kolmogorov-Sina\"i (KS) entropy. We outline how the
approach can be used to investigate the problem of entropy production in a
relativistic heavy-ion reaction from first principles. Finally we discuss some
recent results on entropy production in the strong coupling limit, as obtained
from AdS/CFT duality.
