Models of the four currently recognized regimes of astrochemistry are compared with observations. Ion-Molecule Gas Phase Chemistry is fundamental throughout all interstellar and circumstellar molecular clouds, and by itself explains fairly well the simpler molecular species in diffuse and cold quiescent dense interstellar clouds, as well as in the outer envelopes of circumstellar clouds. Dust-Grain Chemistry may modify ion-molecule chemistry noticeably in regions containing UV radiation, shocks, or other heating agents which can serve to promote surface reactions and to desorb molecules frozen on grains; it likely plays no role in cold quiescent clouds except to adsorb gas phase molecules. Shock Chemistry occurs in regions of star formation and appears important in explaining certain molecular species and in disrupting grains. Circumstellar envelopes combine several chemistries, including those of thermochemical equilibrium in the dense inner regions, and ion-molecule in the outer regions, with grain processes also likely. The limitations of all current models are lack of knowledge of reaction rates, of detailed physical conditions (interstellar clouds), and of the relative depletions (onto grains) of the chemical elements, as well as grain surface chemistry in general. In both interstellar and circumstellar objects, ion-molecule gas phase models are now quite successful in explaining, semi-quantitatively, observed species with up to 4 atoms, but difficulties remain for larger species, as well as the state of carbon, and the models are not yet very predictive.