Emerging data indicate that SARS-CoV-2-specific CD8⁺ T cells targeting different viral proteins are detectable in up to 70% of convalescent individuals^{, , , –}. However, very little information is currently available about the abundance, phenotype, functional capacity and fate of pre-existing and induced SARS-CoV-2-specific CD8⁺ T cell responses during the natural course of SARS-CoV-2 infection. Here, we define a set of optimal and dominant SARS-CoV-2-specific CD8⁺ T cell epitopes. We also perform a high-resolution ex vivo analysis of pre-existing and induced SARS-CoV-2-specific CD8⁺ T cells, applying peptide-loaded major histocompatibility complex class I (pMHCI) tetramer technology. We observe rapid induction, prolonged contraction and emergence of heterogeneous and functionally competent cross-reactive and induced memory CD8⁺ T cell responses in cross-sectionally analyzed individuals with mild disease following SARS-CoV-2 infection and three individuals longitudinally assessed for their T cells pre- and post-SARS-CoV-2 infection. SARS-CoV-2-specific memory CD8⁺ T cells exhibited functional characteristics comparable to influenza-specific CD8⁺ T cells and were detectable in SARS-CoV-2 convalescent individuals who were seronegative for anti-SARS-CoV-2 antibodies targeting spike (S) and nucleoprotein (N). These results define cross-reactive and induced SARS-CoV-2-specific CD8⁺ T cell responses as potentially important determinants of immune protection in mild SARS-CoV-2 infection.