There is a well-accepted prescription for the formation of disk galaxies. The dark matter context works well. Dark potential wells develop hierarchically and acquire angular momentum via tidal torques with neighbouring protohalos. Baryons cool and dissipate their gravitational potential energy, and conserve angular momentum to form a nearly self-gravitating disk of size Rh, where is the dimensionless spin parameter acquired via nonlinear interactions and Rh is the halo virial radius. The disk cools and becomes gravitationally unstable to massive cloud formation. The clouds eventually themselves become unstable and fragment into stars that form a disk with an exponential surface brightness profile, a scale-length of a few kiloparsecs, and a central surface density of order hundreds of solar masses per square parsec for Milky-Way type spirals. Star formation, fed and self-regulated by disk instability, continues via ongoing accretion of gas into the disk from the halo reservoir of gas and small satellites.
There are numerous observational probes of this simple picture. The current star formation rate in disks is measured via H emission, effectively probing the formation of massive stars. The disk gas fraction is measured via HI and CO observations, and provides the fuel that drives disk star formation. Multicolour imaging provides a measure of the spectral energy distribution, and probes the disk age over 10 Gyr. Stellar absorption features such as the Balmer spectral line index H measure ages over a baseline of about 2 Gyr. Large samples of disk galaxies, most recently utilizing the Sloan Digital Sky Survey, enable one to correlate surface brightness with total stellar mass, galaxy radii and colours. 21 cm and H studies probe rotation curves, and allow one to explore the Tully-Fisher relation. Galaxy scales, metallicities and correlations provide fossilized glimpses of the galaxy formation epoch. Observations at high redshift can directly target the epoch of formation. All of these probes lead to strong constraints on the basic disk formation model.
Theory provides a well-accepted framework for the hierarchical formation of dark matter halos. However it is far weaker when it comes to the formation and evolution of the star-forming components of galaxies. In this review, I will concentrate on disk galaxies, and discuss the problems that have arisen with some of the proposed solutions. Much of our understanding centres on the concept of self-regulation of the global star formation rate. Unfortunately, some of the key ingredients are poorly known.