Stars, planets and massive black holes are ubiquitous in binary and multiple configurations. In stellar systems the binary components interact through various type of mass loss and mass transfer. Mass transfer interactions in eccentric systems are in principle phase-dependent and can occur in different ways. We formulate the understanding of mass transfer interactions in binary systems and investigate how these affect their evolution and therefore their observed orbital properties. We present a theoretical framework to describe this evolution and investigate various types of mass transfer including commonly studied cases: isotropic and non-anisotropic wind mass loss; Roche-lobe-overflow; and Bondi-Hoyle accretion. We provide analytical equations of the phase-dependent and long-term (secular) evolution of mass-transferring eccentric binaries. The theoreticalf ramework provided could be implemented in future work in numerical codes widely used to study stellar binary evolution. In the planetary world giant exoplanets could be found so close to their host star that they are expected to start transferring mass to their stellar companion.We investigate the fate of roche-lobe overflowing giant exoplanets andexplore the final orbits of their remnants, trying to provide aplausible theoretical explanation to the observed systems by the planet-hunting mission "Kepler". Massive black hole binary configurations inthe nuclei of large-scale structures like galaxies are formed through galaxy mergers. We explore the evolution of massive black hole binaries in galactic nuclei as a function of the properties of the host andmerging galaxy and attempt to provide an explanation for a number ofobservations, including the puzzling discovery of multiple nuclei in thecore of the brightest galaxies.