HIV persists within the body despite successful suppression of virus replication with antiretroviral therapy (ART). HIV lurks in latent and active reservoirs, leading to rebound of virus spread if ART is interrupted. The latent HIV reservoir is a natural consequence of the life cycle of HIV, with integration of HIV into the genomes of cells that are or later enter the resting state, resulting in transcriptionally quiescent provirus. Resting CD4 T cells comprise the majority of the latent reservoir, although new evidence points to additional, smaller cellular reservoirs of latent HIV. An alternate, so-called active reservoir of HIV also exists within cells such as those found the B cell follicle of lymph nodes, where expression of HIV RNA can be found, again despite the full suppression of viremia and viral replication. Multiple factors such as the degree of virus exposure, timing of ART, and host factors can influence the size and characteristics of the HIV reservoir. Constructing effective strategies for HIV eradication and measuring their impact will require a sophisticated knowledge of the HIV reservoir.