Despite significant advances in our understanding of HIV, a cure has not been realized for the more than 34 million infected with this virus. HIV is incurable because infected individuals harbor cells where the HIV provirus is integrated into the host's DNA but is not actively replicating and thus is not inhibited by antiviral drugs. Similarly, these latent viruses are not detected by the immune system. In this Review, we discuss HIV-1 latency and the mechanisms that allow this pathogenic retrovirus to hide and persist by exploiting the cellular vehicles of immunological memory.