  From a hydrodynamicist's point of view the inclusion of viscosity concepts in
the macroscopic theory of the cosmic fluid would appear most natural, as an
ideal fluid is after all an abstraction (excluding special cases such as
superconductivity). Making use of modern observational results for the Hubble
parameter plus standard Friedmann formalism, we may extrapolate the description
of the universe back in time up to the inflationary era, or we may go to the
opposite extreme and analyze the probable ultimate fate of the universe. In
this review we discuss a variety of topics in cosmology when it is enlarged in
order to contain a bulk viscosity. Various forms of this viscosity, when
expressed in terms of the fluid density or the Hubble parameter, are discussed.
Furthermore, we consider homogeneous as well as inhomogeneous equations of
state. We investigate viscous cosmology in the early universe, examining the
viscosity effects on the various inflationary observables. Additionally, we
study viscous cosmology in the late universe, containing current acceleration
and the possible future singularities, and we investigate how one may even
unify inflationary and late-time acceleration. Finally, we analyze the
viscosity-induced crossing through the quintessence-phantom divide, we examine
the realization of viscosity-driven cosmological bounces, and we briefly
discuss how the Cardy-Verlinde formula is affected by viscosity.
