The evolution of a globular cluster is dominated by the gravitational interaction between the component stars in the cluster. The overall structure of the cluster as well as the dynamics of most of the stars in the cluster are determined by simple -body gravitational dynamics. However, the evolutionary time scales of stellar evolution are comparable to the relaxation time and core collapse time of the cluster. Consequently, stellar evolution affects the masses of the component stars of the cluster, which affects the dynamical state of the cluster. Thus, the dynamical evolution of the cluster is coupled to the evolutionary state of the stars. Also, as we have seen in the previous section, stellar evolution governs the state of the binary evolution and binaries provide a means of support against core collapse. Thus, the details of binary evolution as coupled with stellar evolution must also be incorporated into any realistic model of the dynamical evolution of globular clusters. To close the loop, the dynamical evolution of the globular cluster affects the distribution and population of the binary systems in the cluster. In our case, we are interested in the end products of binary evolution, which are tied both to stellar evolution and to the dynamical evolution of the globular cluster. To synthesize the population of relativistic binaries, we need to look at the dynamical evolution of the globular cluster as well as the evolution of the binaries in the cluster.
General approaches to this problem involve solving the -body problem for the component stars in the cluster and introducing binary and stellar evolution when appropriate to modify the -body evolution. There are two fundamental approaches to tackling this problem - direct integration of the equations of motion for all bodies in the system and large- techniques, such as Fokker-Planck approximations coupled with Monte Carlo treatments of binaries (see Heggie et al.  for a comparison of these techniques). In the next two subsections, we discuss the basics of each approach and their successes and shortfalls. We conclude this section with a discussion of the recent relativistic binary population syntheses generated by dynamical simulations.