New particle formation by nucleation of gas-phase species significantly influences the size distributions and number concentrations of atmospheric aerosols. These nucleated particles are formed at rates that are orders of magnitude higher than were predicted by early models and grow at rates that are typically ten times faster than can be explained by the condensation of sulfuric acid alone. The resultant aerosols exert a significant impact on global climate by affecting the earth's radiation balance directly through the scattering and absorption of incident solar radiation, and indirectly through their role as cloud condensation nuclei (CCN). High formation rates and fast growth to CCN sizes ensure that NPF contributes significantly to the global CCN population. It is the primary goal of the research described in this thesis to develop robust models, constrained by measurement, for the sequential formation of CCN from the nucleation of gas-phase precursors. To this end, my thesis focuses on four topics: the development of nucleation rate parameterizations from correlations between formation rates of 1 nm particles and gas-phase sulfuric acid concentrations in diverse environments; the development of a cluster formation mechanism incorporating energetic barriers at the smallest clusters; the derivation of a simple, dimensionless criterion determining whether or not NPF would occur on a particular day; and the determination of the survival probability of newly formed particles (3 nm) as they grow to a CCN-active size (100 nm).