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Star formation lies at the center of a web of processes that drive cosmicevolution: generation of radiant energy, synthesis of elements, formation ofplanets, and development of life. Decades of observations have yielded avariety of empirical rules about how it operates, but at present we have nocomprehensive, quantitative theory. In this review I discuss the current stateof the field of star formation, focusing on three central questions: whatcontrols the rate at which gas in a galaxy converts to stars? What determineshow those stars are clustered, and what fraction of the stellar population endsup in gravitationally-bound structures? What determines the stellar initialmass function, and does it vary with star-forming environment? I use thesethree question as a lens to introduce the basics of star formation, beginningwith a review of the observational phenomenology and the basic physicalprocesses. I then review the status of current theories that attempt to solveeach of the three problems, pointing out links between them and opportunitiesfor theoretical and numerical work that crosses the scale between them. Iconclude with a discussion of prospects for theoretical progress in the comingyears.

The Big Problems in Star Formation: the Star Formation Rate, Stellar Clustering, and the Initial Mass Function