Gravitational wave detectors such as LIGO are poised to detect signals from coalescing binary black hole systems. Such a detection would allow for the first time a test of general relativity in the strong-field regime. We discuss a number of related problems that must be solved in order to carry out this program successfully. First, we present a numerical simulation of a 15-orbit quasicircular equal mass nonspinning binary black hole system. Different uncertainties in the phase of the extracted and extrapolated gravitational waveforms are discussed. The phase and the amplitude of analytical post-Newtonian approximations of the gravitational waveforms are compared to the phase and amplitude of the numerical gravitational waveforms extrapolated to infinity. The comparison establishes the regime where post-Newtonian theory is accurate, and suggests ways to improving the wave templates used in searches. Pade resummation techniques have been used by the community in constructing templates. We study this technique and show its limitations. Finally, we study how to generalize the concept of eccentricity to the relativistic case. We estimate the precession of a binary system and compare various post-Newtonian precession formula.