  We review the state of the art of active fluids with particular attention to
hydrodynamic continuous models and to the use of Lattice Boltzmann Methods
(LBM) in this field. We present the thermodynamics of active fluids, in terms
of liquid crystals modelling adapted to describe large-scale organization of
active systems, as well as other effective phenomenological models. We discuss
how LBM can be implemented to solve the hydrodynamics of active matter,
starting from the case of a simple fluid, for which we explicitly recover the
continuous equations by means of Chapman-Enskog expansion. Going beyond this
simple case, we summarize how LBM can be used to treat complex and active
fluids. We then review recent developments concerning some relevant topics in
active matter that have been studied by means of LBM: spontaneous flow,
self-propelled droplets, active emulsions, rheology, active turbulence, and
active colloids.
