  Slim accretion disks idea emerged over 30 years ago as an answer to several
unsolved problems. Since that time there was a tremendous increase in the
amount of observational data where this model applies. However, many critical
issues on the theoretical side remain unsolved, as they are inherently
difficult. This is the issue of the disk stability under the radiation
pressure, the role of the magnetic field in the energy transfer inside the disk
and the formation (or not) of a warm corona, and outflows. Thus the progress
has to be done both through further developments of the model and through the
careful comparison to the observational data.
