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The present-day properties of disk galaxies are a consequence both of the initial conditions under which they formed and their dynamical evolution, which is affected by both internally- and externally-driven processes. In this review, I focus principally on the evolution of an isolated disk, especially the dynamical effects of spiral patterns.

Historical computer simulations of isolated, globally-stable, self-gravitating disks (Miller, Prendergast & Quirk 1970; Hockney & Brownrigg 1974; etc.) exhibited transient spiral patterns for at least a few tens of galaxy rotations. Modern simulations of forming galaxies (e.g., Gottlöber et al. 2002; Abadi et al. 2003; Governato et al. 2004, 2007) exhibit similar behavior, but include so many different physical processes that it is unclear which is responsible for the spiral patterns.

It has long been hoped that the spontaneous formation of short-lived spiral patterns in simulations reflects the behavior in real galaxies, although our single snapshot view of every galaxy precludes a direct determination of the lifetimes of individual spiral patterns in galaxies (but see Meidt et al. 2007). An alternative theory (e.g. Bertin & Lin 1996) argues that most spirals should be long-lived, quasi-stationary features, but no observational test has yet been able to determine which picture is correct. The difference between these two points of view is important since the predictions for the evolution of galaxy disks differ substantially.