Numerical models offer powerful insights into tectonic processes, especially when their validity can be tested against geological and geophysical observations from natural orogenic belts. Here we explain some of the criteria for success in integrating orogenic models with data, using examples from the Grenville Orogen. Model designs must be simplified by comparison with nature to illuminate the first-order processes that control orogenic evolution, which limits the extent to which model results can reproduce geological observations. For the western Grenville Orogen, observed variations in geological properties are represented by lower crustal blocks with strength decreasing from the exterior to the interior of the model. GO-series models with this design reproduce the first-order crustal architecture of the Georgian Bay and Montréal – Val d’Or Lithoprobe transects. Both constant-convergence and stop-convergence models produce similar geometries, but only stop-convergence models produce normal-sense shear zones like those observed. EGO-series models, incorporating an initial weak zone bounded by stronger lower crustal blocks, predict exhumation of high-pressure rocks as observed in the eastern Grenville Orogen, although other aspects of these model results are not as successful. The single most important test of a geodynamic model is its ability to integrate diverse and independent observations in a self-consistent manner. Other criteria include consistency with crustal-scale geometry and structural and metamorphic histories. By these criteria, the present models account reasonably well for the syn- and post-convergent evolution of the western Grenville Orogen, but further work is required to produce a fully satisfactory model for the eastern end of the system.