Regeneration is widely distributed among the metazoans. However, clear differences exist as to the degree of regenerative capacity: some phyla can only replace missing body parts, whereas others can generate entirely new individuals. Ascidians are animals that possess a remarkable regenerative plasticity and exhibit a great diversity of mechanisms for asexual propagation and survival. They are marine invertebrate members of the subphylum Tunicata and represent modern-day descendants of the chordate ancestor; in their tadpole stage they exhibit a chordate body plan that is resorbed during metamorphosis. Solitary species grow into an adult that can reach several centimeters in length, whereas colonial species grow by asexual propagation, creating a colony of genetically identical individuals. In this review, we present an overview of the biology of colonial ascidians as a paradigm for study in stem cell and regenerative biology. Focusing on botryllid ascidians, we introduce the potential roles played by multipotent epithelia and multipotent/pluripotent stem cells as source of asexual propagation and regenerative plasticity in the different budding mechanisms, and consider the putative mechanism of body repatterning in a non-embryonic scenario. We also discuss the involvement of intra-colony homeostatic processes in regulating budding potential, and the functional link between allorecognition, chimerism, and regenerative potential.