A curative therapy for HIV-1 infection will have to include measures to eliminate the reservoir of latently HIV- 1 infected cells that allow the virus to persist despite otherwise successful therapy. To date, all efforts to deplete the latent reservoir by triggering viral reactivation have used preexisting drugs that are believed to potentially target molecular mechanisms controlling HIV-1 infection. These therapeutic attempts were not clinically successful. Only in the last few years have cellular models of latent HIV-1 infection suitable for high throughput screening been developed and concerted drug discovery efforts were initiated to discover new HIV-1 reactivating drugs. We here provide a historic overview about the development of cell models with latent HIV-1 infection that lend themselves to drug discovery. We provide an overview from the first reported latently infected cell lines to current in vitro models of latent HIV-1 infection in primary T cells, and compare their potential to be used in future large-scale drug screening efforts.