The GAIA mission will produce an extraordinary database from which weshould be able to deduce not only the Galaxy's current structure, butalso much of its history, and thus cast a powerful light on the way inwhich galaxies in general are made up of components, and of how theseformed. The database can be fully exploited only by fitting to it asophisticated model of the entire Galaxy. Steady-state models are offundamental importance even though the Galaxy cannot be in a steadystate. A very elaborate model of the Galaxy will be required toreproduce the great wealth of detail that GAIA will reveal. Asystematic approach to model-building will be required if such a modelis to be successfully constructed, however. The natural strategy is toproceed through a series of models of ever increasing elaborateness,and to be guided in the specification of the next model by mismatchesbetween the data and the current model.An approach to the dynamics of systems with steady gravitationalpotentials that we call the "torus programme" promises to provide anappropriate framework within which to carry out the proposed modellingprogramme. The basic principles of this approach have been worked outin some detail and are summarized here. Some extensions will berequired before the GAIA database can be successfullyconfronted. Other modelling techniques that might be employed arebriefly examined.