Virus-specific CD8⁺ T cells that differentiate in the context of resolved versus persisting infections exhibit divergent phenotypic and functional characteristics, which suggests that their differentiation trajectories are governed by distinct cellular dynamics, developmental pathways and molecular mechanisms. For acute infection, it is long known that antigen-specific T cell populations contain terminally differentiated effector T cells, known as short-lived effector T cells, and proliferation-competent and differentiation-competent memory precursor T cells. More recently, it was identified that a similar functional segregation occurs in chronic infections. A failure to generate proliferation-competent precursor cells in chronic infections and tumors results in the collapse of the T cell response. Thus, these precursor cells are major therapeutic and prophylactic targets of immune interventions. These observations suggest substantial commonality between T cell responses in acute and chronic infections but there are also critical differences. We are therefore reviewing the common features and peculiarities of precursor cells in acute infections, different types of persistent infection and cancer.