HIV is a highly mutable virus, which evades natural and vaccine-induced immune responses and is the causative agent for the AIDS epidemic.  I will describe methods, rooted in statistical physics, which aim to determine the fitness landscape of HIV – i.e., a definition of the collective sets of mutations that allow the virus to maintain fitness and evade immunity, and those combinations of mutations that cripple it.  The “Hamiltonian” that describes this fitness landscape is analogous to the Hopfield Hamiltonian for associative memory in neural networks.  I will show how this Hamiltonian reveals encoded “memories” in the HIV population of host-pathogen riposte won by the virus, and scaling laws that describe this phenomenon.  I will also present how evolutionary dynamics with our inferred fitness landscape can predict HIV evolution in individual patients, and how we have harnessed this knowledge, along with other experimental tests, to design a therapeutic vaccine against HIV which is being advanced to pre-clinical trials.