In the absence of treatment, HIV-1 infection, usually starting with a single virion, leads inexorably to a catastrophic decline in the numbers of CD4(+) T cells and to AIDS, characterized by numerous opportunistic infections as well as other symptoms, including dementia and wasting. In the 30 years since the AIDS pandemic came to our attention, we have learned a remarkable amount about HIV-1, the responsible virus--the molecular details about how it functions and interacts with the host cell, its evolution within the host, and the countermeasures it has evolved to overcome host defenses against viral infection. Despite these advances, we remain remarkably ignorant about how HIV-1 infection leads to disease and the death of the human host. In this brief article, we introduce and discuss important lessons that we have learned by examining the dynamics of viral populations and infected cells. These studies have revealed important features of the virus-host interaction that now form the basis of our understanding of the importance and consequence of ongoing viral replication during HIV-1 infection.