  The main subject of this thesis rests on the study ---at different levels of
description--- of instabilities in systems which are driven, i.e., maintained
far from equilibrium by an external forcing. We focus here on two main classes,
namely, driven--diffusive fluids and driven granular gases.
  A particular driven-diffusive lattice model, prototype for nonequilibrium
phase transitions, is investigated. A well-known disadvantage of lattice models
is that, when they are compared directly with experiment, often do not account
for important features of the corresponding nonequilibrium phase diagram, such
as structural, morphological, and even critical properties. Furthermore,
theoreticians often tend to consider them as prototypical models for certain
behavior, a fact which is in many cases not justified. This is discussed in the
first part of this thesis, where we introduce a novel, realistic model for
computer simulation of anisotropic fluids.
  The second class of systems we consider in this thesis concerns driven
granular gases. We study clustering, symmetry breaking, and phase separation
instabilities in two-dimensional driven granular gases, using both molecular
dynamics simulations and granular hydrodynamics. Hydrostatic predictions are
tested by comparing with molecular dynamics simulations. We are able to develop
an effective Langevin description for close-packed macroparticle, confined by a
harmonic potential and driven by a delta-correlated noise.
