The reservoir of human immunodeficiency virus type 1 (HIV-1), a long-lived pool of latently infected cells harboring replication-competent viruses, is the major obstacle to curing acquired immune deficiency syndrome (AIDS). Although the combination antiretroviral therapy (cART) can successfully suppress HIV-1 viremia and significantly delay the progression of the disease, it cannot eliminate the viral reservoir and the patient must continue to take anti-viral medicines for life. Currently, the appearance of the ‘Berlin patient’, the ‘Boston patients’, and the ‘Mississippi baby’ have inspired many therapeutic strategies for HIV-1 aimed at curing efforts. However, the specific eradication of viral latency and the recovery and optimization of the HIV-1-specific immune surveillance are major challenges to achieving such a cure. Here, we summarize recent studies addressing the mechanisms underlying the viral latency and define two categories of viral reservoir: ‘shallow’ and ‘deep’. We also present the current strategies and recent advances in the development of a functional cure for HIV-1, focusing on full/partial replacement of the immune system, ‘shock and kill’, and ‘permanent silencing’ approaches.