Some of the most exciting scientific objectives for LISA involve the search for, and detailed study of, signals from sources that contain MBHs (e.g. black holes with mass greater than 10^6 solar masses. The coalescence of MBH-MBH binaries will be the brightest events visible to LISA. While ground-based interferometers may or may not even see comparable mass black hole mergers, for LISA, the signal-to-noise ratios for super-massive BBH events should be quite high, up to 10^4. In this case the BBH events may be so strong and numerous that the ability to make observations of other weaker sources depends on filtering out the BBH signals according to accurate model waveforms. Because the new ground-based interferometers are already beginning operations and because model information may be critical even in the developmental stages of the LISA mission, there is a pressing need to produce at least moderately accurate models for BBH coalescence immediately. Detailed comparison with numerical simulations will reveal the masses, spins and orientations of the two black holes, providing crucial information about the history and formation of the binary system. It will also provide an important precision test of dynamical nonlinear gravity, predicted by Einstein's general theory of relativity. Our research focus on a newly introduced a new combined approach to the binary black hole modeling problem, which is dubbed the Lazarus Project, a technique that bridges far and close limit approximation approaches with full numerical relativity to solve Einstein equations applied in the truly nonlinear dynamical regime. Using this approach one can in fact model supermassive binary black hole systems and provided the first approximate theoretical estimates for the gravitational radiation waveforms and energy that are generated during the coalescence. In the picture Gravitational waves (in red) are produced as two black holes spiral together and collide in this computer simulation (using the so-called Lazarus approach). Colors in the picture represent the strength of the "wave component" of the gravitational field. After the collision, the gravitational waves travel outward in all directions, eventually arriving in our solar system where they can be measured by detectors. Another set of guaranteed sources for LISA is stellar mass compact objects (white dwarfs, neutron stars, black holes) inspiralling into massive black holes in galactic nuclei. In general relativity, test particles follow geodesics of the spacetime. Clearly, solar mass objects spiralling into massive black holes cannot be treated as test particles, but as ``almost'' test particles, perturbed from their geodesics by recoil forces from the gravitational radiation, i.e. by radiation reaction (in fact, the particles motion is also perturbed by so-called conservative self-forces which are not associated with gravitational radiation, although the term radiation reaction is often used to denote both radiative and conservative corrections to the particle motion). One can therefore use perturbation theory around a single black hole to compute gravitational radiation from such extreme mass ratio binary systems. The small mass ratio of these binary systems provides the expansion parameter for the perturbative analysis of the attendant gravitational radiation.