The adaptive immune system is important for control of most viral infections. The three fundamental components of the adaptive immune system are B cells (the source of antibodies), CD4 T cells, and CD8 T cells. The armamentarium of B cells, CD4 T cells, and CD8 T cells has differing roles in different viral infections and in vaccines, and thus it is critical to directly study adaptive immunity to SARS-CoV-2 to understand COVID-19. Knowledge is now available on relationships between antigen-specific immune responses and SARS-CoV-2 infection. Although more studies are needed, a picture has begun to emerge that reveals that CD4 T cells, CD8 T cells, and neutralizing antibodies all contribute to control of SARS-CoV-2 in both non-hospitalized and hospitalized cases of COVID-19. The specific functions and kinetics of these adaptive immune responses are discussed, as well as their interplay with innate immunity and implications for COVID-19 vaccines and immune memory against re-infection.