It is interesting if there exist non-trivial relations between ultraviolet complete quantum gravity and its low energy effective field theories (EFTs). Such relations are so-called swampland conditions. In this talk, we will develop a method to derive swampland conditions by extending so-called S-matrix positivity bounds to gravitational context. In our formulation, several working assumptions on quantum gravity S-matrix such as unitarity and the Reggeization of graviton exchange are imposed. We will then discuss the implications of positivity bounds on gravitational EFTs. First, we will demonstrate that our bounds are indeed satisfied in the Standard Model. Next, we will show that our bounds provide strong constraints on dark photon models which can be tested against on-going future experiments. This implies the possibility of probing quantum gravity from low-energy observables and the phenomenological importance of studying the properties of quantum gravity S-matrix.