As ground-based gravitational wave detectors are searching for gravitational waves at their design sensitivity and plans for future space-based detectors are underway, it is important to have accurate theoretical models of the expected gravitational waves to be able to detect potential signals and extract information from the measured data. This thesis contains work on developing theoretical tools for modeling the expected gravitational waves from two different classes of sources, which are key targets for current and future gravitational wave detectors. The work is based on four papers in collaboration with 'Eanna Flanagan. (i) We show that ground-based gravitational wave detectors may be able to constrain the nuclear equation of state using the early, relatively clean portion of the signal of detected neutron star ? neutron star inspirals.

(ii) The second class of gravitational wave source we consider are radiation - reaction driven inspirals of test particles into much more massive black holes. Chapter 5 contains our work on developing a rigorous formalism based on two-timescale expansions for treating the evolving orbit. Our results provide a clarification of the existing prescription for computing the leading order orbital motion and resolve the difficulties with previous approaches for going beyond leading order.

(iii) In Chapter 6, we analyze the effect of gravitational radiation reaction on generic orbits around a body with an axisymmetric mass quadrupole moment Q to linear order in Q, to linear order in the mass ratio and in the weak-field limit. In addition we consider a system of two point masses where one body has a single mass multipole or current multipole. We show that within our approximations the motion is not integrable (except for the cases of spin and mass quadrupole).

(iv) Chapter 7 gives an alternative derivation of the result of Sago for an explicit expression for the time-averaged rate of change of the Carter constant (a third constant of geodesic motion around a rotating black hole in addition to energy and axial angular momentum) in the adiabatic limit which is formulated in terms of sums over modes and can be used for numerically computing leading order waveforms.