The paucity of observed dwarf galaxies in the Local Group relative to the abundance of predicted dark matter halos remains one of the greatest puzzles of the ΛCDM paradigm. Solving this puzzle now requires not only matching the numbers of objects but also understanding the details of their star formation histories. We present a summary of such histories derived from the HST data using the color-magnitude diagram fitting method. To reduce observational uncertainties, we condense the data into five cumulative parameters: the fractions of stellar mass formed in the last 1, 2, 5, and 10 Gyr, and the mean stellar age. We interpret the new data with a phenomenological model based on the mass assembly histories of dark matter halos and the Schmidt law of star formation. The model correctly predicts the radial distribution of the dwarfs and the fractions of stars formed in the last 5 and 10 Gyr. However, in order to be consistent with the observations, the model requires a significant amount of recent star formation in the last 2 Gyr. Within the framework of our model, this prolonged star formation can be achieved by adding a stochastic variation in the density threshold of the star formation law. The model results are not sensitive to late gas accretion, the slope of the Schmidt law, or the details of cosmic reionization. A few discrepancies still remain: our model typically predicts too large stellar masses, only a modest population of ultrafaint dwarfs, and a small number of dwarfs with anomalously young stellar populations. Nevertheless, the observed star formation histories of Local Group dwarfs are generally consistent the expected star formation in cold dark matter halos.