Tunicates encompass a large group of marine filter-feeding animals and more than half of them are able to reproduce asexually by a particular form of nonembryonic development (NED) generally called budding. The phylogeny of tunicates suggests that asexual reproduction is an evolutionarily plastic trait, a view that is further reinforced by the fact that budding mechanisms differ from one species to another, involving nonhomologous tissues and cells. In this review, we explore more than 150 years of literature to provide an overview of NED diversity and we present a comparative picture of budding tissues across tunicates. Based on the phylogenetic relationships between budding and nonbudding species, we hypothesize that NED diversity is the result of seven independent acquisitions and subsequent diversifications in the course of tunicate evolution. While this scenario represents the state-of-the-art of our current knowledge, we point out gray areas that need to be further explored to refine our understanding of tunicate phylogeny and NED. Tunicates, with their plastic evolution and diversity of budding, represent an ideal playground for evolutionary developmental biologists to unravel the genetic and molecular mechanisms regulating nonembryonic development, as well as to better understand how such a profound innovation in life-history has evolved in numerous metazoans.