Antiretroviral therapy (ART) effectively reduces cycles of viral replication but does not target proviral populations in cells that persist for prolonged periods and that can undergo clonal expansion. Consequently, chronic human immunodeficiency virus (HIV) infection is sustained during ART by a reservoir of long-lived latently infected cells and their progeny. This proviral landscape undergoes change over time on ART. One of the forces driving change in the landscape is the clonal expansion of infected CD4 T cells, which presents a key obstacle to HIV eradication. Potential mechanisms of clonal expansion include general immune activation, antigenic stimulation, homeostatic proliferation, and provirus-driven clonal expansion, each of which likely contributes in varying, and largely unmeasured, amounts to maintaining the reservoir. The role of clinical events, such as infections or neoplasms, in driving these mechanisms remains uncertain, but characterizing these forces may shed light on approaches to effectively eradicate HIV. A limited number of individuals have been cured of HIV infection in the setting of bone marrow transplant; information from these and other studies may identify the means to eradicate or control the virus without ART. In this review, we describe the mechanisms of HIV-1 persistence and clonal expansion, along with the attempts to modify these factors as part of reservoir reduction and cure strategies.