Consistency of properties is critical for materials performance, and fundamentally depends on the microstructure on the level of the grains. The evolution of the grain structure is governed by the grain boundary energy and mobility, both functions on the five-dimensional space of grain boundary parameters. Despite decades of experimental effort, the properties of these functions in most regions of the space remain unknown. The result is that existing simulations of grain structure evolution usually employ simple analytic formulas for the grain boundary energy and mobility, and cannot quantitatively reproduce experimental grain structure evolution. Microstructure information made available by recently-developed three-dimensional microscopy techniques could soon be used to infer more realistic grain boundary energy and mobility functions. However, existing front-tracking codes generally make assumptions about the grain boundary network topology that are inconsistent with the microstructures that could arise, or restrict the allowed topological transitions to a small set that could cause substantial deviations from experimental trajectories. This talk will outline our recent efforts to substantially expand the allowed sets of grain boundary topologies and topological transitions, to formulate a physical criterion for the selection of a topological transition, and to develop equations of motion suitable for arbitrary grain boundary energies and mobilities. The intention is to prepare a front-tracking code able to perform predictive simulations of grain structure evolution on the day that realistic grain boundary energy and mobility functions become available.