SARS-CoV-2 Delta and Omicron strains are the most globally relevant variants of concern (VOCs). While individuals infected with Delta are at risk to develop severe lung disease 1 , Omicron infection causes less severe disease, mostly upper respiratory symptoms 2,3 . The question arises whether rampant spread of Omicron could lead to mass immunization, accelerating the end of the pandemic. Here we show that infection with Delta, but not Omicron, induces broad immunity in mice. While sera from Omicron-infected mice only neutralize Omicron, sera from Delta-infected mice are broadly effective against Delta and other VOCs, including Omicron. This is not observed with the WA1 ancestral strain, although both WA1 and Delta elicited a highly pro-inflammatory cytokine response and replicated to similar titers in the respiratory tracts and lungs of infected mice as well as in human airway organoids. Pulmonary viral replication, pro-inflammatory cytokine expression, and overall disease progression are markedly reduced with Omicron infection. Analysis of human sera from Omicron and Delta breakthrough cases reveals effective cross-variant neutralization induced by both viruses in vaccinated individuals. Together, our results indicate that Omicron infection enhances preexisting immunity elicited by vaccines, but on its own may not induce broad, cross-neutralizing humoral immunity in unvaccinated individuals.