The mirrors flown in the Chandra Observatory are, without doubt, some of the most exquisite optics ever flown on a space mission. Their angular resolution is matched by no other X-ray observatory, existing or planned. The promise of that performance, along with a goal of achieving 1% calibration of the optics' characteristics, led to a decision early in the construction and assembly phase of the mission to develop an accurate and detailed model of the optics and their support structure. This model has served in both engineering and scientific capacities; as a cross-check of the design and a predictor of scientific performance; as a driver of the ground calibration effort; and as a diagnostic of the as-built performance. Finally, it serves, directly and indirectly, as the primary vehicle with which Chandra observers interpret the contribution of the optics' characteristics to their data. We present the underlying concepts in the model, as well the mechanical, engineering and metrology inputs. We discuss its use during ground calibration and as a characterization of on-orbit performance. Finally, we present measures of the model's accuracy, where further improvements may be made, and its applicability to other missions.