I will discuss different aspects of G-fluxes in F-theory compactifications on compact singular elliptic Calabi-Yau fourfolds. The main focus of my talk will be on the effect of G-fluxes on the low-energy effective action of F-theory. I will elude on the holomorphic coupling functions of the 4D N=1 supergravity theory, namely the superpotential and the gauge coupling function, as induced and corrected by background fluxes and their backreactions. I will also address the computation of the chiral index of charged matter in global F-theory compactifications and the cancelation of anomalies by a generalized Green-Schwarz mechanism. For the entire discussion the duality to M-theory on the resolved smooth elliptic Calabi-Yau fourfold as studied in the effective 3D N=2 supergravity theory on its Coulomb branch will be essential.