Spirals in galaxies have long been thought to be caused by gravitational instability in the stellar component of the disk, but discerning the precise mechanism had proved elusive. Tidal interactions, and perhaps bars, may provoke some spiral responses, but spirals in many galaxies must be self-excited. We survey the relevant observational data and aspects of disk dynamical theory. The origin of the recurring spiral patterns in simulations of isolated disk galaxies has recently become clear, and it is likely that the mechanism is the same in real galaxies, although evidence to confirm this supposition is hard to obtain. As transient spiral activity increases random motion, the patterns must fade over time unless the disk also contains a dissipative gas component. Continuing spiral activity alters the structure of the disks in other ways: reducing metallicity gradients and flattening rotation curves are two of the most significant. The overwhelming majority of spirals in galaxies have two- or three-fold rotational symmetry, indicating that the cool, thin disk component is massive. Spirals in simulations of halo-dominated disks instead manifest many arms and, consequently, do not capture the expected full spiral-driven evolution. We conclude by identifying areas where further work is needed.