  This dissertation is written as an annotated collection of selected articles.
The dissertation focuses on the modelling of accretion disks in X-ray binaries
with a black hole or neutron star. The main objective is to use advanced
numerical methods to reveal the fundamental processes that influence the
observed spectral and temporal features. Among the significant results of this
modelling is the recognition of the puffy accretion disk, a novel type of
accretion disk based purely on the results of numerical simulations.
Furthermore, the work focuses on modelling the X-ray variability and
quasi-periodic oscillations using analytical models of accretion disks, but an
advanced description of the oscillations, and a discussion of the implications
of this modelling for observational data.
