Latently infected CD4⁺ T cells are the main barrier to complete clearance of HIV infection, but it is unclear what mechanisms govern latent HIV infection in vivo. To address this question, we developed a new panel of reverse transcription droplet digital polymerase chain reaction (RT-ddPCR) assays specific for different HIV transcripts that define distinct blocks to transcription. We applied this panel of assays to CD4⁺ T cells freshly isolated from HIV-infected patients on suppressive antiretroviral therapy (ART) to quantify the degree to which different mechanisms inhibit HIV transcription. In addition, we measured the degree to which these transcriptional blocks could be reversed ex vivo by T cell activation (using anti-CD3/CD28 antibodies) or latency-reversing agents. We found that the main reversible block to HIV RNA transcription was not inhibition of transcriptional initiation but rather a series of blocks to proximal elongation, distal transcription/polyadenylation (completion), and multiple splicing. Cell dilution experiments suggested that these mechanisms operated in most of the HIV-infected CD4⁺ T cells examined. Latency-reversing agents exerted differential effects on the three blocks to HIV transcription, suggesting that these blocks may be governed by different mechanisms.