The HIV cascade--often referred to as "the HIV continuum"--provides a valuable framework for population-level representations of engagement with the HIV healthcare system. The importance and appeal of this framework are evidenced by a large body of scientific literature, as well as by the adoption of cascade-related indicators by medical and public health organizations worldwide. Despite its centrality in the fields of HIV treatment and prevention, however, the traditional cascade provides limited description of the processes affecting the numbers it represents. Representations that describe these processes and capture the dynamic nature of HIV-infected persons' pathways through the healthcare system are essential for monitoring and predicting intervention effects and epidemic trends. We propose here a complementary schema--termed the "HIV States and Transitions" framework--designed to maintain key strengths of the traditional cascade while addressing key limitations and more fully describing the dynamic aspects of HIV testing, care, and treatment at the population level.