The reionization of the all-pervading intergalactic medium (IGM) is a landmark event in the history of cosmological structure formation. Studies of Gunn-Peterson absorption in the spectra of distant quasars show that hydrogen is highly photoionized out to redshift z > 6, while polarization data from the Wilkinson Microwave Anisotropy Probe (WMAP) constrain the redshift of a sudden reionization event to be significantly higher, z =11 +/- 1.5. It is generally thought that the IGM is kept ionized by the integrated UV emission from active nuclei and star-forming galaxies, but the relative contributions of these sources as a function of epoch are poorly known. In this talk I review the theories behind UV/X-ray background models, and describe new solutions of the radiative transfer of ionizing background radiation in a clumpy, expanding medium. I present improved synthesis models of the UV/X-ray cosmic background spectrum and its evolution, discussing several astrophysical consequences and possible tests.