The Joint United Nations Programme on HIV/AIDS (UNAIDS) recently updated its global targets for antiretroviral therapy (ART) coverage for HIV-positive persons under which 90% of HIV-positive people are tested, 90% of those are on ART, and 90% of those achieve viral suppression. Treatment policy is moving toward treating all HIV-infected persons regardless of CD4 cell count—otherwise known as treatment as prevention—in order to realize the full therapeutic and preventive benefits of ART. Mathematical models have played an important role in guiding the development of these policies by projecting long-term health impacts and cost-effectiveness. To guide future policy, new mathematical models must consider the barriers patients face in receiving and taking ART. Here, we describe the HIV care cascade and ART delivery supply chain to examine how mathematical modeling can provide insight into cost-effective strategies for scaling-up ART coverage in sub-Saharan Africa and help achieve universal ART coverage.