During its hot, dense, early evolution the Universe was a primordial nuclear reactor, synthesizing the light nuclides D, He-3, He-4 and Li-7 in the first thousand seconds. The presently observed abundances of these relic nuclides provide a unique window on the early Universe. The implications of current observations for cosmology (the universal density of nucleons) and for particle physics (new particles beyond the standard model) will be reviewed. The present data appear to be in rough agreement with the predictions of the standard, hot, big bang model for three species of light neutrinos, and a nucleon-to-photon ratio restricted to a narrow range of 3-4 parts in 10 billion. On closer inspection, however, a tension is revealed between the inferred primordial abundances of deuterium and helium-4. Although observations of deuterium in nearly primordial, high-redshift QSO absorbers may help to relieve this tension, current data appear to exacerbate the crisis. Resolution of this conflict may lie with the data (statistical uncertainties?), with the analysis of the data (systematic uncertainties?), or with the fundamental physics (massive, unstable, and/or degenerate neutrinos?). Independent (non-BBN) evidence from cosmological observations of large scale dynamics and structure may be useful in deciding among the current options.