The optical properties of materials, such as magnetic metals or magnetic semiconductors, having simultaneously negative electrical and magnetic permeabilities are considered. One finds that the refractive index with respect to vacuum is negative; that the Poynting vector and the wave vector of propagating EM waves have opposite signs; that the sign of the Doppler effect is opposite that, for ordinary materials and that the Cherenkov radiation cone is directed backwards rather than forwards. Finally, the question of the mechanical forces arising from EM propagation in materials having a negative refractive index is discussed.