  We review spectral theory of soliton gases in integrable dispersive
hydrodynamic systems. We first present a phenomenological approach based on the
consideration of phase shifts in pairwise soliton collisions and leading to the
kinetic equation for a non-equilibrium soliton gas. Then a more detailed theory
is presented in which soliton gas dynamics are modelled by a thermodynamic type
limit of modulated finite-gap spectral solutions of the Korteweg-de Vries and
the focusing nonlinear Schr\"odinger equations. For the focusing nonlinear
Schr\"odinger equation the notions of soliton condensate and breather gas are
introduced that are related to the phenomena of spontaneous modulational
instability and the rogue wave formation. Integrability properties of the
kinetic equation for soliton gas are discussed and some physically relevant
solutions are presented and compared with direct numerical simulations of
dispersive hydrodynamic systems.
