A cure for HIV infection remains elusive due to the persistence of replication-competent HIV proviral DNA during suppressive antiretroviral therapy (ART). With the exception of rare elite or post-treatment controllers of viremia, withdrawal of ART invariably results in the rebound of viremia and progression of HIV disease. A thorough understanding of the reservoir is necessary to develop new strategies in order to reduce or eliminate the reservoir. However, there is significant heterogeneity in the sequence composition, genomic location, stability, and expression of the HIV reservoir both within and across individuals, and a majority of proviral sequences are replication-defective. These factors, and the low frequency of persistently infected cells in individuals on suppressive ART, make understanding the reservoir and its response to experimental reservoir reduction interventions challenging. Here, we review the characteristics of the HIV reservoir, state-of-the-art assays to measure and characterize the reservoir, and how these assays can be applied to accurately detect reductions in reservoir during efforts to develop a cure for HIV infection. In particular, we highlight recent advances in the development of direct measures of provirus, including intact proviral DNA assays and full-length HIV DNA sequencing with integration site analysis. We also focus on novel techniques to quantitate persistent and inducible HIV, including RNA sequencing and RNA/gag protein staining techniques, as well as modified viral outgrowth methods that seek to improve upon throughput, sensitivity and dynamic range.