  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 (FNLS) equations. For the FNLS 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.
