  In this thesis, I study hydrodynamical models of slim accretion disks ---
advective, optically thick disks which generalize the standard models of
radiatively efficient thin disks to all accretion rates. I start with a general
introduction to the theory of accretion onto compact objects. It is followed by
a derivation of the commonly-used standard models of thin disks. In the
subsequent section I introduce the equations describing slim disks, explain the
numerical methods I used to solve them and discuss properties of such
solutions. I also give a general derivation of non-stationary equations and
present the time evolution of thermally unstable accretion disks. I introduce a
state-of-the-art approach coupling the radial and vertical structures of an
advective accretion disk and discuss the improvements it brings to
vertically-averaged solutions. I also present a numerical model of
self-illuminated slim accretion disks. Finally, I present and discuss
applications of slim accretion disks: estimating of spin of the central black
hole in LMC X-3 through X-ray continuum fitting basing on high-luminosity data,
spinning-up of black holes by super-critical accretion flows and normalizing of
magnetohydrodynamical global simulations.
