Memory CD8 T cells are an important component of protective immunity against viral infections, and understanding their development will aid in the design of optimal vaccines. Recent work has shed light on the complex differentiation process that occurs during a CD8 T-cell response to viral infection. Dramatic cellular changes occur as T cells transition through the three characteristic phases of an antiviral response, initial activation and expansion, the death phase, and the formation of memory T cells. Each of these three phases of the T-cell response is accompanied by extensive transcriptional and functional changes that result in naïve T cells expanding and gaining effector functions, survival of 5 to 10% of the effectors through the death phase, and the gradual acquisition of memory properties by the surviving virus-specific T cells. This review will discuss our current understanding of how functional and protective CD8 T-cell responses are generated and maintained following different types of infections. Viral infections can be largely divided into two types:(i) acute infections, where virus is eliminated; and (ii) chronic infections, where virus persists. This second type of infection may be further classified into latent infections and those in which there is persistent viral replication. While acute infections usually result in effective antiviral immune responses, chronic infections can be associated with suboptimal T-cell function. We will first focus on acute infections and on recent work that has led to our current understanding of the CD8 T-cell differentiation program that occurs when antigen is eliminated following initial infection and then discuss how CD8 T-cell responses can be altered and impaired during chronic infections when virus persists.