As the early Universe evolved from hot and dense to cool and dilute, it passed through a short-lived epoch when conditions of temperature and density permitted the synthesis of astrophysically interesting abundances of D, 3He, 4He, and 7Li. At present, observations of these nuclides in a variety of astrophysical sites (stars, Galactic and extragalactic H II regions, QSOALS, etc.) have permitted quite precise estimates of their primordial abundances, opening a window on early-universe cosmology and providing constraints on physics beyond the standard models of cosmology and particle physics. The relic abundances of D, 3He, and 7Li are nuclear reaction rate limited, providing good probes of the nucleon density when the universe was less than a half hour old. This is complementary to baryon density estimates from the CBR, whose information was encoded some 400 kyr later, and to those provided by observations of the current or recent universe, 13 Gyr after BBN. Of these light nuclides, D is the baryometer of choice and current estimates of the relic abundance, yD = 2.6 ± 0.4, suggest a baryon to photon ratio, unchanged from BBN to the present, of 10 = 6.1 ± 0.6, in excellent agreement with the WMAP and LSS determined value of 10 = 6.14 ± 0.25. For this choice (S = 1, e = 0), the less well constrained relic abundance of 3He (y3 = 1.1 ± 0.2)  is also in agreement with its SBBN expected value. These successes for the standard models are tempered by the challenges posed by 4He and 7Li. The SBBN predicted 4He mass fraction, YP = 0.248, differs from the observationally inferred primordial abundance adopted here, YP = 0.241 ± 0.004, by nearly 2. However, as discussed in Section 3.3, the uncertainties in YP are likely dominated by systematic, not statistical errors, so it is difficult to know if this tension between D (and 3He and the CBR) and 4He is cause for serious concern. In contrast to the other light nuclides, the BBN abundance of 4He is insensitive to the nuclear reaction rates and, hence, to the nucleon density at BBN. YP is largely set by the neutron to proton ratio at BBN, so that 4He is an excellent probe of the weak interactions and of the early Universe expansion rate. Perhaps the 4He challenge to SBBN is a signal of new physics. The SBBN predicted abundance of 7Li ([Li]P = 2.65-0.06+0.05) is nearly a factor of two higher than the observationally determined value  ([Li]P = 2.37 ± 0.05). While there is some spread in the lithium abundances inferred from the data , the largest cause for concern is that Li is observed in the oldest stars in the Galaxy, which have had ample time to modify their original surfaces abundances. For 7Li, it appears likely that astrophysical uncertainties dominate at present.
Thus, while there appears to be qualitative confirmation of the standard models of cosmology and particle physics extrapolated back to the first seconds of the evolution of the Universe, precision should not be confused with accuracy. The accuracy of the presently-inferred primordial abundances of D, 3He, 4He, and 7Li remains in question and it would not be at all surprising if one or more of them changed by more than the presently-quoted errors. After all, there are only 5 (6) lines of sight where deuterium is observed in high-redshift, relatively unprocessed (low metallicity) material; 3He is only observed in the chemically processed interstellar medium of the Galaxy and the lack of variation of its abundance with metallicity or with position in the Galaxy suggest a very delicate balance between post-BBN production, destruction and survival; systematic errors and corrections to the 4He abundance inferred from observations of low metallicity, extragalactic H II regions are likely larger, maybe much larger, than the current statistical uncertainties; lithium is derived from observations of very old, very low metallicity stars (good!) in our Galaxy (bad?) and the corrections for stellar atmosphere models and, especially, for main sequence mixing-induced depletion and destruction remain large and uncertain. Much interesting, important work remains for observational and theoretical astronomers.
The current standard models receive strong support from these messengers from the early universe, confirming in broad outline our understanding of the evolution of the Universe and the particles in it, from the first seconds to the present. Any models of new physics must consider this success and avoid introducing new conflicts. Much interesting, important work remains for cosmologists and high energy theorists.
I am grateful to all those I've collaborated with over the years on the subject of this review. Discussions with J. E. Felten, K. A. Olive, E. D. Skillman, M. Tosi, D. Tytler, and J. K. Webb were especially valuable in its preparation. My research is supported by a grant (DE-FG02-91ER40690) from the US Department of Energy.