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SARS-CoV-2 variants of concern exhibit varying degrees of transmissibility and, in some cases, escape from acquired immunity. Much effort has been devoted to measuring these phenotypes, but understanding their impact on the course of the pandemic—especially that of immune escape—has remained a challenge. Here, we use a mathematical model to simulate the dynamics of wild-type and variant strains of SARS-CoV-2 in the context of vaccine rollout and nonpharmaceutical interventions. We show that variants with enhanced transmissibility frequently increase epidemic severity, whereas those with partial immune escape either fail to spread widely or primarily cause reinfections and breakthrough infections. However, when these phenotypes are combined, a variant can continue spreading even as immunity builds up in the population, limiting the impact of vaccination and exacerbating the epidemic. These findings help explain the trajectories of past and present SARS-CoV-2 variants and may inform variant assessment and response in the future. [Display omitted] • Modeled impacts of different SARS-CoV-2 variants across range of scenarios • Enhanced transmissibility leads to more infections and narrows margin for control • Partial immune escape often remains rare and may not limit vaccination impact • Impact of immune escape is much greater when paired with enhanced transmissibility A modeling approach looking at the impact of SARS-CoV-2 variants with partial immune escape and/or increased transmissibility suggests that enhanced transmissibility is more strongly linked to epidemic severity and narrows the margin for control. [ABSTRACT FROM AUTHOR]