Eradication of latent human immunodeficiency virus (HIV) infection is a global health challenge. Reactivation of HIV latency and killing of virus-infected cells, the so-called “kick and kill” or “shock and kill” approaches, are a popular strategy for HIV cure. While antiretroviral therapy (ART) halts HIV replication by targeting multiple steps in the HIV life cycle, including viral entry, integration, replication, and production, it cannot get rid of the occult provirus incorporated into the host-cell genome. These latent proviruses are replication-competent and can rebound in cases of ART interruption or cessation. In general, a very small population of cells harbor provirus, serve as reservoirs in ART-controlled HIV subjects, and are capable of expressing little to no HIV RNA or proteins. Beyond the canonical resting memory CD4+ T cells, HIV reservoirs also exist within tissue macrophages, myeloid cells, brain microglial cells, gut epithelial cells, and hematopoietic stem cells (HSCs). Despite a lack of active viral production, latently HIV-infected subjects continue to exhibit aberrant cellular signaling and metabolic dysfunction, leading to minor to major cellular and systemic complications or comorbidities. These include genomic DNA damage; telomere attrition; mitochondrial dysfunction; premature aging; and lymphocytic, cardiac, renal, hepatic, or pulmonary dysfunctions. Therefore, the arcane machineries involved in HIV latency and its reversal warrant further studies to identify the cryptic mechanisms of HIV reservoir formation and clearance. In this review, we discuss several molecules and signaling pathways, some of which have dual roles in maintaining or reversing HIV latency and reservoirs, and describe some evolving strategies and possible approaches to eliminate viral reservoirs and, ultimately, cure/eradicate HIV infection.