  Hard models for particle interactions have played a crucial role in the
understanding of the structure of condensed matter. In particular, they help to
explain the formation of oriented phases in liquids made of anisotropic
molecules or colloidal particles, and continue to be of great interest in the
formulation of theories for liquids in bulk, near interfaces and in biophysical
environments. Hard models of anisotropic particles give rise to complex phase
diagrams, including uniaxial and biaxial nematic phases, discotic phases, and
spatially ordered phases such as smectic, columnar or crystal. Also, their
mixtures exhibit additional interesting behaviours where demixing competes with
orientational order. Here we review the different models of hard particles used
in the theory of bulk anisotropic liquids, leaving aside interfacial
properties, and discuss the associated theoretical approaches and computer
simulations, focusing on applications in equilibrium situations. The latter
include one-component bulk fluids, mixtures and polydisperse fluids, both in
two and three dimensions, and emphasis is put on liquid-crystal phase
transitions and complex phase behaviour in general.
