The latent HIV-1 reservoir in blood decays very slowly, even during prolonged suppression of viral replication by antiretroviral therapy (ART). Mechanisms for reservoir persistence include replenishment through low-level viral replication, longevity and homeostatic proliferation of memory T cells, and most recently appreciated, clonal expansion of HIV-infected cells. Clonally expanded cells make up a large and increasing fraction of the residual infected cell population on ART, and insertion of HIV proviruses into certain host cellular genes has been associated with this proliferation. That the vast majority of proviruses are defective clouds our assessment of the degree to which clonally expanded cells harbor infectious viruses, and thus the extent to which they contribute to reservoirs relevant to curing infection. This review summarizes past studies that have defined our current understanding and the gaps in our knowledge of the mechanisms by which proviral integration and clonal expansion sustain the HIV reservoir.