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Black holes play a central role in astrophysics and in physics more generally. Candidate black holes are nearly ubiquitous in nature. They are found in the cores of nearly all galaxies, and appear to have resided there since the earliest cosmic times. They are also found throughout the galactic disk as companions to massive stars. Though these objects are almost certainly black holes, their properties are not very well constrained. We know their masses (often with errors that are factors of a few), and we know that they are dense. In only a handful of cases do we have information about their spins. Gravitational-wave measurements will enable us to rectify this situation. Focusing largely on measurements with the planned space-based detector LISA, I will describe how gravitational-wave measurements will allow us to measure both the masses and spins of black holes with percent-level accuracy even to high redshift, allowing us to track their growth and evolution over cosmic time. I will also describe how a special class of sources will allow us to measure the multipolar structure of candidate black hole spacetimes. This will make it possible to test the no-hair theorem, and thereby to test the hypothesis that black hole candidates are in fact black holes are described by general relativity.

Recent numerical simulations of spinning binary black holes have found that the orbital plane tends to bob up and down in phase with the orbit. It will be shown that similar effects occur in nearly all relativistic systems. The reasons for this are essentially kinematic and appear unrelated to those leading to the final "kicks" observed after merger. Simple examples are provided for binary systems bound together by gravitational electromagnetic and mechanical forces.

We present a second order perturbative formalism that includeperturbative spin effects and apply it to the computation of recoil velocites of merging binary black holes and to the computation of waveforms from small mass ratio binaries.

Gravitational wave data analysis of compact binary systems requires the use of matched filtering. This technique cross-correlates the data stream with a certain template that characterizes the gravitational wave signal. Successful parameterestimation thus requires an accurate model of the gravitational wave template. In this talk I will describe a new fast and accurate technique to model the gravitational wave signal from extreme-mass ratio inspirals. Such events consisting of a neutron star or solar mass black hole spiraling into a supermassive black hole are staple sources of the Laser Interferometer Space Antenna. This new model combines the effective-one-body formalism of post-Newtonian theory and black hole perturbation theory leading to accurate waveforms both when the supermassive black hole spins and when it does not.