  This paper is devoted to memory of late Professor V. G. Bagrov, who was my
first teacher in theoretical physics. About 45 years later, theoretical physics
has changed and me too. The subject of this paper relates some old ideas in
cosmology with some recent ideas, as is reflected in the title. The current
status of Starobinsky inflation is reviewed and compared to three main
conjectures in the Swampland program. It is argued that the Starobinsky
inflation model is not in conflict with those Swampland conjectures in their
basic versions.
