The block-and-lock strategy aims to achieve a functional cure for human immunodeficiency virus type 1 (HIV-1) infection by enforcing durable, drug-independent silencing of proviral transcription. Several latency-promoting agents have been described that effectively limit viral reactivation in vitro or in animal models. However, most approaches induce only partial or reversible transcriptional repression and have not yet been translated into safe and effective clinical interventions. This review summarizes the molecular mechanisms underlying block-and-lock strategies and critically evaluates the limitations of current candidate compounds. We highlight recent advances in understanding HIV-1 integration site selection, focusing on the roles of lens epithelium-derived growth factor p75 (LEDGF/p75) and cleavage and polyadenylation specificity factor subunit 6 (CPSF6) in directing proviral integration toward gene-dense, transcriptionally active chromatin. Pharmacological disruption of the LEDGF/p75–integrase interaction by LEDGF/p75 inhibitors (LEDGINs) redirects proviral integration toward less transcriptionally active genomic regions that are more resistant to reactivation. Recent tandem knockout studies, however, demonstrate that CPSF6 plays a dominant role in guiding HIV-1 integration toward gene-dense, transcriptionally active chromatin. LEDGIN treatment has been linked to the preferential targeting of proviruses to heterochromatin-rich regions within the nuclear interior. By contrast, CPSF6 knockout redirects integration toward peripheral heterochromatin, especially lamina-associated domains (LADs), genomic regions typically exhibiting stronger and more stable transcriptional repression than interior heterochromatin. These findings suggest that therapeutic modulation of CPSF6 may exert a more profound and durable effect on proviral silencing within a block-and-lock framework. Nevertheless, complete CPSF6 ablation is associated with severe cellular toxicity. The challenges associated with CPSF6-related adverse effects and potential strategies to overcome these limitations are discussed.