The interplay between immune response and HIV is intensely studied via mathematical modeling, with significant insights but few direct answers. Here in this short review, we highlight advances and knowledge gaps across different aspects of immunity. In particular, we identify the innate immune response and its role in priming the adaptive response as ripe for modeling. The latter have been the focus of most modeling studies, but we also synthesize key outstanding questions regarding effector mechanisms of cellular immunity and development of broadly neutralizing antibodies. Thus far, most modeling studies aimed to infer general immune mechanisms
we foresee that significant progress will be made next by detailed quantitative fitting of models to data, and prediction of immune responses.