Antiretroviral therapy can completely suppress HIV replication below the limit of detection for sustained periods of time, but cannot eradicate the virus from silent reservoirs. Accordingly, life-long therapy is needed and interruption of therapy always leads to resurgence of viral spread and disease. Several approaches have been suggested to eliminate silently infected cells or the HIV genomes integrated in these cells. These approaches are currently mostly at the stage of basic research or early preclinical development and need to be developed in the translational chain. While significant knowledge exists about the nature of silent reservoirs, the number and clonality of viral integration sites is currently largely unknown and needs to be further investigated to develop virus eradication strategies and therapies.