During an infection, antigen‐specific CD8⁺ T cells undergo numerous cellular and transcriptional changes as they develop from naive T cells into effector and memory cells. However, when the antigen persists in a chronic infection, the cellular programs governing effector and memory development are influenced by chronic stimulation, and dysfunctional or exhausted CD8⁺ T cells are generated. Recently, exhausted CD8⁺ T cells were found to differ dramatically from naive and functional memory CD8⁺ T cells on a transcriptional level, demonstrating that exposure to chronic antigen can impact T cells at a fundamental level. While transcriptional changes in CD8⁺ T cells during memory development is currently a topic of particular interest, the transcriptional changes related to exhaustion and other forms of T‐cell dysfunction have received less attention. New computational methods are not only uncovering important transcription factors in these developmental processes but are also going further to define and connect these transcription factors into transcriptional modules that work in parallel to control cell fate and state. Understanding the molecular processes behind the development of CD8⁺ T‐cell memory and exhaustion should not only increase our understanding of the immune system but also could reveal therapeutic targets and treatments for infectious and immunological diseases. Here, we provide a basic overview of acute and chronic viral infections and the transcription factors known to influence the development of virus‐specific T cells in both settings. We also discuss recent innovations in genomic and computational tools that could be used to enhance the way we understand the development of T‐cell responses to infectious disease.