Despite the introduction of combinatory antiretroviral therapy (cART), HIV-1 infection cannot be cured and is still one of the major health issues worldwide. Indeed, as soon as cART is interrupted, a rapid rebound of viremia is observed. The establishment of viral latency and the persistence of the virus in cellular reservoirs constitute the main barrier to HIV eradication. For this reason, new therapeutic approaches have emerged to purge or restrain the HIV-1 reservoirs in order to cure infected patients. However, the viral latency is a multifactorial process that depends on various cellular mechanisms. Since these new therapies mainly target viral transcription, their development requires a detailed and precise understanding of the regulatory mechanism underlying HIV-1 transcription. In this review, we discuss the complex molecular transcriptional network regulating HIV-1 gene expression by focusing on the involvement of host cell factors that could be used as potential drug targets to design new therapeutic strategies and, to a larger extent, to reach an HIV-1 functional cure.