Starobinsky inflation and Swampland conjectures

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.