The concept of slim accretion disks emerged over 30 years ago as an answer to several unsolved problems. Since that time there has been 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 radiation pressure, the role of the magnetic field in the energy transfer inside the disk, 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 careful comparison with the observational data.