Galaxies are distributed throughout the Universe in a clustering hierarchy. A large majority of bright galaxies are disk-shaped, with a significant minority being ellipsoidal. The question of how these objects came into existence is the subject of intense current research. However, it has become increasingly clear that the present-day properties of galaxies were not exclusively laid down at the time of their formation, and that internally-driven processes have contributed significantly to their present properties. This review describes, from a theoretical perspective, the dynamical behavior that is believed to be important in restructuring galaxy disks from their initially endowed properties. Kormendy & Kennicutt (2004), updated in Kormendy (2012), give a comprehensive review of the same topic from an observer's perspective. The present-day properties of galaxy disks were recently reviewed by van der Kruit & Freeman (2011).
It has to be said at the outset that galaxies do not first form, and then evolve, in temporally distinct phases. In fact, even today formation is incomplete for many galaxies, such as the Milky Way. However, the balance has clearly shifted from the rapid collapse and merging picture that characterized the roughly first one third of the life of the Universe to more quiescent evolution over the remaining two thirds. The vibrant topic of galaxy formation is too large to be included in any detail in this review, yet it cannot be omitted entirely as it provides the context for galaxy evolution.
After the initial collapse, and every subsequent major merger event, gas begins to settle into a disk whose orientation is determined by the angular momentum that it acquired from the tidal fields of other nearby mass concentrations. The thinness of galaxy disks requires there to have been a protracted period of quiescent evolution, during which a number of internally-driven processes gradually rearrange the structure of galaxies. These include disk growth through slow accretion of gas, the formation and evolution of bars, recurring spiral instabilities, the response of the stellar system to the radial rearrangement of matter, especially the gas, etc. These, together with the influence of the environment, drive what has become known as "secular evolution," by which is meant the gradual restructuring of a galaxy over time scales much longer than a crossing time. Evolution is mostly driven by the outward redistribution of angular momentum in a galaxy, which enables it to reach a state of lower energy, and such changes are prolonged by gas accretion.
Note that the word "secular" has a narrow meaning in classical studies of rotating fluid spheroids by Maclaurin and Jacobi (summarized by Chandrasekhar 1987). They revealed that viscosity, a dissipative process, can destabilize some rotating Maclaurin spheroids, which become secularly unstable and evolve to Jacobi ellipsoids. However, the same Maclaurin spheroid could be dynamically stable in the absence of viscosity. In this review, I adopt the deliberately broader and vaguer meaning of secular explained in the previous paragraph.
Of the many processes discussed in this review, I here highlight two of particular significance. Spiral patterns are probably the most important agent of secular evolution. They have long been known to redistribute angular momentum and to cause the random motions of stars to increase over time, but we now know that they cause extensive radial mixing of both the stars and the gas, and they smooth small-scale irregularities in the mass distribution. Bars also cause substantial secular changes. Once formed, stellar bars in isolated, gas-free disks simply rotate steadily with no tendency to evolve (e.g. Miller & Smith 1979), but interaction with gas and other mass components of the galaxy can gradually alter the properties of the bar, with evolutionary consequences for its host galaxy. It is noteworthy that the rate of secular evolution by both spirals and bars is substantially accelerated by a moderate fraction of gas.
In order to keep to a manageable length, I focus here on secular evolution in galaxy disks largely driven through internal processes. In appropriate places I mention environmental factors, such as the infall of debris, tidal interactions, etc., which can also alter the structure of a galaxy. But describing the full extent to which environmental factors may drive evolution would stray into the domain of galaxy assembly and would add too much to the length of this review.