The hot big‐bang cosmology provides a reliable accounting of the Universe from about 10−2sec after the bang until the present, as well as a robust framework for speculating back to times as early as 10−43sec. Cosmology faces a number of important challenges; foremost among them are determining the quantity and composition of matter in the Universe and developing a detailed and coherent picture of how structure (galaxies, clusters of galaxies, superclusters, voids, great walls, and so on) developed. At present there is a working hypothesis—cold dark matter—which is based upon inflation and which, if correct, would extend the big bang model back to 10−32sec and cast important light on the unification of the forces. Many experiments and observations, from CBR anisotropy experiments to Hubble Space Telescope observations to experiments at Fermilab and CERN, are now putting the cold dark matter theory to the test. At present it appears that the theory is viable only if the Hubble constant is smaller than current measurements indicate (around 30 km s−1Mpc−1), or if the theory is modified slightly, e.g., by the addition of a cosmological constant, a small admixture of hot dark matter (5 eV ‘‘worth of neutrinos’’), more relativistic particle or a tilted spectrum of density perturbations.