Adult T-cell leukemia (ATL) and HTLV-1-associated Myelopathy/Tropical Spastic Paraparesis (HAM/TSP) are the two main diseases that are caused by the HTLV-1 virus. One of the features of HTLV-1 infection is its resistance against programmed cell death, which maintains the survival of cells to oncogenic transformation and underlies the viruses’ therapeutic resistance. Two main genes by which the virus develops cancer are Tax and HBZ; playing an essential role in angiogenesis in regulating viral transcription and modulating multiple host factors as well as apoptosis pathways. Here we have reviewed by prior research how the apoptosis pathways are suppressed by the Tax and HBZ and new drugs which have been designed to deal with this suppression.