Despite our ability to suppress HIV-1 replication indefinitely in people on optimal combined antiretroviral therapy (cART), HIV-1 persists as a stably integrated and replication-competent provirus in a heterogeneous collection of long-lived cells (often referred to as 'latent reservoirs') in all individuals on treatment. Reactivation of these latent proviruses is believed to be responsible for the rebound viraemia that can be seen in nearly all people following treatment cessation. Hence, the persistence of HIV-1 in latent reservoirs remains one of the greatest challenges in current HIV cure research. Latent HIV-1 reservoirs are established early during the acute phase of the infection, possibly before the virus appears in the systemic circulation. As well as the issue of timing, we review the proposed hypotheses on the mechanisms by which this latent state is believed to be established early in the course of the infection and the effect of early initiation of cART on the size and stability of these reservoirs. We conclude that prevention of the establishment of latent HIV-1 reservoirs by even extremely early initiation of cART proves to be practically impossible. However, early treatment initiation remains one of the crucial interventions needed to achieve the ultimate goal of a functional cure for HIV-1 infection because of its ability to reduce the overall size of HIV-1 reservoirs. Together with other interventions, early cART initiation may thus eventually lead to a state of better control over the residual amount of virus in the body, allowing people to stay off treatment for prolonged periods of time.