Humanity is currently facing the challenge of two devastating pandemics caused by two very different RNA viruses: HIV-1, which has been with us for decades, and SARS-CoV-2, which has swept the world in the course of a single year. The same evolutionary strategies that drive HIV-1 evolution are at play in SARS-CoV-2. Single nucleotide mutations, multi-base insertions and deletions, recombination, and variation in surface glycans all generate the variability that, guided by natural selection, enables both HIV-1's extraordinary diversity and SARS-CoV-2's slower pace of mutation accumulation. Even though SARS-CoV-2 diversity is more limited, recently emergent SARS-CoV-2 variants carry Spike mutations that have important phenotypic consequences in terms of both antibody resistance and enhanced infectivity. We review and compare how these mutational patterns manifest in these two distinct viruses to provide the variability that fuels their evolution by natural selection.