Galaxies in the modern Universe demonstrate very diverse shapes. They can be one-component stellar spheroids (elliptical galaxies) or complex systems including compact stellar spheroids in the centers and extended flat stellar disks (spiral and lenticular galaxies). The morphology of the galaxies is related with other physical parameters: rotation velocities, current star formation rates, and stellar population ages. The problem of morphological type origin is persistently discussed for the last hundred years, and the dominant paradigm changes every time. Last years it becomes clear that the main agent of galaxy evolution is non-stop outer matter accretion; hence it is just the time to associate the morphological type origin with the properties of this outer accretion and with its secular change during billion years of the Universe evolution.