How can we formulate appropriate equations that are able to provide a realistic and quantitative description of the processes involved in the dynamics of galaxies? How should we model specific phenomena, such as the occurrence of spiral structure or the equilibrium configuration that underlies the observed photometric properties of elliptical galaxies? The modeling process can be articulated in two steps: (1) choice of equations and (2) identification of the relevant basic state and parameter characterizations. Because we are dealing with extremely complex and composite systems (which include different populations of stars, gas in various forms, magnetic fields, etc.), we should recognize from the beginning that no matter how detailed we try to be, we are introducing only model equations, that is, equations for ideal systems that have only some of the ingredients of the real systems we would like to describe. Once the equations are chosen, a second major aspect of the modeling process is that of choosing a good match to the parameters, boundary conditions, and overall characteristics that define the astrophysical phenomena to be studied.

There is a tradeoff between the number of ingredients that can be included in the equations and the model and what can be practically calculated. Special cases with fewer ingredients may be amenable to exact analytical solutions or to efficient numerical calculations, with the obvious advantages implied by such a possibility.