The principal problems of the matter evolution in hydrodynamic picture of A+A collisions are considered. They concern the process of freeze-out, possible duality in the hydrodynamic and kinetic descriptions, and formation of the initial conditions at pre-thermal partonic stage, in particular, developing of initial transverse velocities and angular momentum. Also time evolution of the momentum spectra, Bose--Einstein correlation functions and averaged phase-space densities (APSD) are analyzed within hydrodynamic and kinetic models. The results shed light on the behavior of the observables, in particular, the interferometry volumes and APSD in A+A collisions at different energies and for different nuclei. The new class of freeze-out parameterizations, accounting for continuous in time particle emission, is considered and their hydrodynamical realization is discussed.

PACS numbers: 24.10.Nz, 24.10.Pa, 25.75.--q, 25.75.Gz