  We use time-frequency methods for the study of Fourier Integral operators
(FIOs). In this paper we shall show that Gabor frames provide very efficient
representations for a large class of FIOs. Indeed, similarly to the case of
shearlets and curvelets frames, the matrix representation of a Fourier Integral
Operator with respect to a Gabor frame is well-organized. This is used as a
powerful tool to study the boundedness of FIOs on modulation spaces. As special
cases, we recapture boundedness results on modulation spaces for
pseudo-differential operators with symbols in $M^{\infty,1}$, for some
unimodular Fourier multipliers and metaplectic operators.
