The present Universe is observed to be expanding and filled with radiation (the 2.7 K cosmic background radiation; CBR) as well as with "ordinary matter" (baryons), "dark matter", and "dark energy". As a consequence, the early Universe must have been hot and dense. Sufficiently early in its evolution, the universal energy density would have been dominated by relativistic particles ("radiation dominated"). During its early evolution the Universe passed through a brief epoch when it functioned as a cosmic nuclear reactor, synthesizing the lightest nuclides: D, 3He, 4He, and 7Li. These relics from the distant past provide a unique window on the early evolution of the Universe, as well as being valuable probes of the standard models of cosmology and particle physics. Comparing the predicted primordial abundances with those inferred from observational data tests the standard models and may uncover clues to their modifications and/or to extensions beyond them. It is clear that Big Bang Nucleosynthesis (BBN), one of the pillars of modern cosmology, has a crucial role to play as the study of the evolution of the Universe enters a new, data-rich era.
As with all science, cosmology depends on the interplay between theoretical ideas and observational data. As new and better data become available, models may need to be refined, revised, or even replaced. A consequence of this is that any review such as this one is merely a signpost along the road to a better understanding of our Universe. While details of the current "standard" model, along with some of its more popular variants to be discussed here, may need to be revised or rejected in the future, the underlying physics to be described here can provide a useful framework and context for understanding those changes. Any quantitative conclusions to be reached today will surely need to be modified in the light of new data. This review is, then, a status report on the standard model, highlighting its successes as well as exposing the current challenges it faces. While we may rejoice in the consistency of the standard model, there is still much work, theoretical and observational, to be done.