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(Abridged) We present a semi-analytic model for Cold Dark Matter halo substructure that can be used as a framework for studying galaxy formation and an ingredient in halo models of galaxy clustering. We perform a comprehensive comparison of the model to the results of a suite of high-resolution cosmological simulations. The comparisons reveal that subhalo statistics, such as velocity and mass functions, radial distributions, and the halo occupation distributions, agree well over three orders of magnitude in host halo mass at various redshifts. Both in the simulations and in our model, the radial distributions of subhalos are significantly shallower than that of the dark matter density. The abundance of subhalos in a host is set by competition between destruction and new accretion. High mass halos and halos at high redshift tend to host more subhalos because the subhalos have, on average, been accreted more recently. Similarly, at fixed mass, halos that formed more recently host more subhalos. Observed "fossil groups" may represent an extreme tail of this correlation. We find a related correlation between host halo concentration and subhalo abundance at fixed host mass, Nsat ~ c^-a, where a changes with redshift and host-to-subhalo mass ratio. Lastly, we use our model to populate host halos in one of our high-resolution cosmological simulations, replacing the subhalos resolved in the simulation with subhalos computed according to our model. We show that the resulting 2pt correlation function of such a "hybrid" halo ensemble is indistinguishable from that measured directly in the simulation. This supports one of the key tenets of the standard halo model -- the assumption that the halo occupation distribution is statistically independent of host halo environment.