The authors investigate the global continuity on L p spaces with p [1, ] of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global L 2 boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hoermander class amplitudes i.e. those in S m , with , [0,1] . They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted L p spaces, L p w with 1