In this talk I will discuss various propagators important in classical and quantum physics of the free scalar field as described by the Klein—Gordon equation. The focus of this talk will be the Feynman propagator. I will show that on static spacetimes the Feynman propagator can be rigorously defined as the limit of the resolvent of the Klein—Gordon operator from above to zero. I will also outline how these results may be extended to some more general spacetimes, thus yielding a distinguished Feynman inverse in such cases.