Antiretroviral therapy cannot cure HIV-1 infection due to the persistence of a small number of latently infected cells harboring replication-competent proviruses. Measuring persistent HIV-1 is challenging, as it consists of a mosaic population of defective and intact proviruses that can shift from a state of latency to active HIV-1 transcription. Due to this complexity, most of the current assays detect multiple categories of persistent HIV-1, leading to an overestimate of the true size of the latent reservoir. Here, we review the development of the viral outgrowth assay, the gold-standard quantification of replication-competent proviruses, and discuss the insights provided by full-length HIV-1 genome sequencing methods, which allowed us to unravel the composition of the proviral landscape. In this review, we provide a dissection of what defines HIV-1 persistence and we examine the unmet needs to measure the efficacy of interventions aimed at eliminating the HIV-1 reservoir.