Antiretroviral therapy (ART) has dramatically improved the prognosis for people living with HIV-1, but a cure remains elusive. The largest barrier to a cure is the presence of a long-lived latent reservoir that persists within a heterogenous mix of cell types and anatomical compartments. Efforts to eradicate the latent reservoir have primarily focused on latency reversal strategies. However, new work has demonstrated that the majority of the long-lived latent reservoir is established near the time of ART initiation, suggesting that it may be possible to pair an intervention with ART initiation to prevent the formation of a sizable fraction of the latent reservoir. Subsequent treatment with latency reversal agents, in combination with immune clearance agents, may then be a more tractable strategy for fully clearing the latent reservoir in people newly initiating ART. Here, we summarize molecular mechanisms of latency establishment and maintenance, ongoing efforts to develop effective latency reversal agents, and newer efforts to design latency prevention agents. An improved understanding of the molecular mechanisms involved in both the establishment and maintenance of latency will aid in the development of new latency prevention and reversal approaches to ultimately eradicate the latent reservoir.