Injury induces retinal Müller glia of certain cold-blooded vertebrates, but not those of mammals, to regenerate neurons. To identify gene regulatory networks that reprogram Müller glia into progenitor cells, we profiled changes in gene expression and chromatin accessibility in Müller glia from zebrafish, chick, and mice in response to different stimuli. We identified evolutionarily conserved and species-specific gene networks controlling glial quiescence, reactivity, and neurogenesis. In zebrafish and chick, the transition from quiescence to reactivity is essential for retinal regeneration, whereas in mice, a dedicated network suppresses neurogenic competence and restores quiescence. Disruption of nuclear factor I transcription factors, which maintain and restore quiescence, induces Müller glia to proliferate and generate neurons in adult mice after injury. These findings may aid in designing therapies to restore retinal neurons lost to degenerative diseases.