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We present a study of key aspects of the evolution of binary stars with emphasis on binaries consisting of two white dwarf stars. The evolution of such systems is driven by the loss of angular momentum by gravitational wave radiation. Effects like mass transfer and other modes of angular momentum loss and redistribution influence the evolutionary fate of the binary, and can lead to a merger, the tidal disruption of one of the components or its survival as a long-lived AM Canum Venaticorum (AM CVn) type system. Our study takes into account some of these effects; like mass loss, tides, accretion disk formation and direct impact accretion. We find that under some circumstances, the tidal coupling between the spin of the components and the orbit of the binary leads to oscillations in the orbital separation and the mass transfer rate. We also find that as compared to previous studies, a larger fraction of the systems should survive to form AM CVn type systems. We also consider systems in which the mass transfer rate exceeds the critical Eddington rate, leading to mass loss from the system. It is possible that some of the lost mass settles into a disk around the binary to form a circumbinary disk. In the second part of the thesis, we present a toy model for disks in general, and find that the coupling of such a circumbinary disk to the binary has a destabilizing effect on the binary.