In this chapter, we explore the topic of matter wave interferometry and of quantum coherence, which plays a central role in quantum theory and is also used for many experimental applications. Atom interferometers are briefly discussed, and decoherence processes are introduced. We then consider decoherence of atom interference fringes, associated with quantum fluctuations of gravitational space-time. In the frame of the quantum theory of gravitation, still under construction, a fluctuating space-time foam should exist at the Planck space-time scale. Based on recent theoretical models, we speculate on the possible observation of quantum gravitational fluctuations, by using matter wave interferometry. Finally, the interference and tunneling of two condensates, confined in nearby potential wells, is considered, and the condensate analogue of Josephson oscillations is described.