When and how did the first stars and black holes form and when and how did they ionize most of the gas in the universe? In this review we have sketched the first attempts to answer these questions and the basic physical principles that underlie these attempts. The coming decade will likely be marked by major advances in our ability to make theoretical predictions in an attempt to answer these questions, and will culminate with the launch of NGST, a telescope which is ideally suited for testing these predictions. At about the same time, the Planck satellite (and perhaps MAP before it) is expected to directly infer the reionization redshift from measurements of the CMB polarization power spectrum on large angular scales. Also in about a decade, next-generation arrays of radio telescopes may detect the 21 cm emission from the pre-reionization, neutral warm IGM. The difficult questions just mentioned will receive their ultimate answers from observations, but it surely is fun to try to find the answers theoretically in advance, before we can deduce them by looking through our most technologically-advanced telescopes.
We thank Tom Abel, Steve Furlanetto, Nick Gnedin, Zoltan Haiman, Piero Madau, Jordi Miralda-Escudé and especially the editor Marc Kamionkowski for providing useful comments after a careful reading of the manuscript. AL thanks the Institute for Advanced Study at Princeton for its kind hospitality when the writing of this review began. RB acknowledges support from Institute Funds; support by the Smithsonian Institution Visitor Program during a visit to the Harvard-Smithsonian CfA; and the hospitality of the Weizmann Institute, Israel, where part of this review was written. This work was supported in part by NASA grants NAG 5-7039, 5-7768, and NSF grants AST-9900877, AST-0071019 for AL.