This chapter explores the effects of gravitational fields on different types of progressive and evanescent vacuum electromagnetic fields. In Sect. 25.1.1, the structure of plane wave solutions to Maxwell’s equations in vacuo is discussed in terms of wave profiles, phase functions and directions of propagation. The solutions are used to generate new solutions given by particular isometries of Minkowski spacetime and are shown to give rise to the relativistic Doppler shift first enunciated by Doppler (1842) and Fizeau (1848) before the advent of Einstein’s Special Relativity. Although the total electromagnetic field energy (defined by a timelike Minkowski Killing vector field) is “unbounded”, it is argued that plane wave Minkowski solutions offer a good approximation in certain domains of Minkowski spacetime. In Sect. 25.1.2, general non-axially symmetric electromagnetic propagating and spatially evanescent vacuum beam solutions in Minkowski spacetime are discussed and in Sect. 25.1.3 the axially symmetric sector is analysed in some detail. In Sect. 25.1.4 we compare vacuum Maxwell plane wave pulse solutions in background Minkowski and Einstein-de Sitter spacetime metrics. In Sect. 25.2 a 6-parameter family of future-pointing timelike geodesics of the Einstein-de Sitter metric is constructed in terms of elliptic functions and a method outlined for their numerical analysis.