Abstract Quasispecies theory revolutionized our understanding of viral evolution by describing viruses as dynamic populations of genetically diverse variants constantly adapting. This article explores the theory’s role in virus-host interactions, including immune evasion, drug resistance, and viral emergence. We review the original model, recent advances, and key virus dynamics needing incorporation into quasispecies theory. We introduce the ultracube concept as a more realistic multidimensional sequence space to investigate virus evolutionary dynamics.