This talk will summarize the major issues surrounding the big bang and highlight some current research on events which occurred during the big bang between the first instants of cosmic expansion and the time of the surface of photon last scattering. Space-time itself, the universe, and almost every form of matter which we are aware of (photons, leptons, baryons, light elements, dark matter, dark energy, etc.) formed and began its evolution during the big bang. Our understanding of these phenomena, however, is constrained by only two means by which one can probe the physics of the big bang. One is the observed power spectrum of temperature fluctuations in the cosmic microwave background radiation. This spectrum derives from a combination of physics from the first instants of cosmic inflation, and the physics of matter and radiation at the photon last scattering epoch. The other probe is the observed ashes of primordial nucleosynthesis which occurred from about 1 sec to 1000 sec into the big bang. This talk summarizes these two cosmic probes and their roles in motivating and constraining new cosmological paradigms. Among the topics discussed are the limits which these probes place upon the nature of dark matter and dark energy, along with possible insights into physics beyond the standard model of particle physics.