The Hubble constant, which measures the expansion rate, together with the total energy density of the Universe, sets the size of the observable Universe, its age, and its radius of curvature. Excellent progress has been made recently toward the measurement of the Hubble constant: a number of different methods for measuring distances have been developed and refined, and a primary project of the Hubble Space Telescope has been the accurate calibration of this difficult-to-measure parameter. The recent progress in these measurements is summarized, and areas where further work is needed are discussed. Currently, for a wide range of possible cosmological models, the Universe appears to have a kinematic age less than about /14+/-2 billion years. Combined with current estimates of stellar ages, the results favor a low-matter-density universe. They are consistent with either an open universe, or a flat universe with a non-zero value of the cosmological constant.