Star formation and the atomic-molecular transition

In the last decade large surveys have allowed us to separate the atomic and molecular phases of the interstellar media in a wide variety of galaxies, and to determine how each of these phases correlates with star formation. The most striking results of these observations have been that the transition from H i to H2 occurs at a characteristic gas column density that depends on metallicity, and that star formation correlates primarily with the molecular phase. These observations have stimulated a burst of theoretical work, which I review here. The work can be broken into three primary questions: what physical mechanisms control the H i to H2 transition? Why does star formation correlate with H2 and not with some other phase of the ISM? Finally, what are the implications of the answers to the previous two questions for our understanding of star formation on the cosmological scale? I discuss our current best answers to each of these questions, and conclude with prospects for future work.