The pandemic of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has motivated an intensive analysis of its molecular epidemiology following its worldwide spread. To understand the early evolutionary events following its emergence, a data set of 985 complete SARS-CoV-2 sequences was assembled. Variants showed a mean of 5.5 to 9.5 nucleotide differences from each other, consistent with a midrange coronavirus substitution rate of 3 × 10^-4 substitutions/site/year. Almost one-half of sequence changes were C→U transitions, with an 8-fold base frequency normalized directional asymmetry between C→U and U→C substitutions. Elevated ratios were observed in other recently emerged coronaviruses (SARS-CoV, Middle East respiratory syndrome [MERS]-CoV), and decreasing ratios were observed in other human coronaviruses (HCoV-NL63, -OC43, -229E, and -HKU1) proportionate to their increasing divergence. C→U transitions underpinned almost one-half of the amino acid differences between SARS-CoV-2 variants and occurred preferentially in both 5' U/A and 3' U/A flanking sequence contexts comparable to favored motifs of human APOBEC3 proteins. Marked base asymmetries observed in nonpandemic human coronaviruses (U ≫ A > G ≫ C) and low G+C contents may represent long-term effects of prolonged C→U hypermutation in their hosts. The evidence that much of sequence change in SARS-CoV-2 and other coronaviruses may be driven by a host APOBEC-like editing process has profound implications for understanding their short- and long-term evolution. Repeated cycles of mutation and reversion in favored mutational hot spots and the widespread occurrence of amino acid changes with no adaptive value for the virus represent a quite different paradigm of virus sequence change from neutral and Darwinian evolutionary frameworks and are not incorporated by standard models used in molecular epidemiology investigations.IMPORTANCE The wealth of accurately curated sequence data for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), its long genome, and its low substitution rate provides a relatively blank canvas with which to investigate effects of mutational and editing processes imposed by the host cell. The finding that a large proportion of sequence change in SARS-CoV-2 in the initial months of the pandemic comprised C→U mutations in a host APOBEC-like context provides evidence for a potent host-driven antiviral editing mechanism against coronaviruses more often associated with antiretroviral defense. In evolutionary terms, the contribution of biased, convergent, and context-dependent mutations to sequence change in SARS-CoV-2 is substantial, and these processes are not incorporated by standard models used in molecular epidemiology investigations.