Since its initial discovery, HIV has infected more than 70 million individuals globally, leading to the deaths of 35 million. At present, the annual number of deaths has significantly decreased due to 75% of HIV-positive individuals being on antiretroviral therapy. Although there is no cure yet, available treatments extend life expectancy, enhance quality of life, and reduce transmission by maintaining viral load below the detection limit of 50 copies/mL, making the individual's levels undetectable and untransmittable. HIV has attracted considerable attention in the computational modeling area, with various models having been developed with different degrees of complexity in an attempt to explain the viral dynamics of the disease. It is important to note that no single model can fully incorporate and predict all the critical factors influencing the dynamics of the disease and its response to treatments. Since the number of published models is large, the purpose of this article is to review several relevant models found in the literature that describe biologically plausible scenarios of HIV infection, including key features of disease progression with or without treatment. A total of 15 models are described, with some implemented in the mrgsolve package in R Studio and shared for the benefit of the scientific community. The modeling framework concerning HIV infection aids in identifying the most impactful parameters within the system and their implications in the model outcomes. Insights provided by these models may help in confirming targets for current and novel therapies, thereby contributing to the exploration of new strategies.