The T cell response plays an indispensable role in the early control and successful clearance of SARS-CoV-2 infection. However, several important questions remain about the role of cellular immunity in COVID-19, including the shape and composition of disease-specific T cell repertoires across convalescent patients and vaccinated individuals, and how pre-existing T cell responses to other pathogens—in particular, common cold coronaviruses—impact susceptibility to SARS-CoV-2 infection and the subsequent course of disease. This review focuses on how the repertoire of T cell receptors (TCR) is shaped by natural infection and vaccination over time. We also summarize current knowledge regarding cross-reactive T cell responses and their protective role, and examine the implications of TCR repertoire diversity and cross-reactivity with regard to the design of vaccines that confer broader protection against SARS-CoV-2 variants.