Nearly half of the animal phyla contain species that propagate asexually via agametic reproduction, often forming colonies of genetically identical modules, that is, ramets, zooids, or polyps. Clonal reproduction, colony formation, and modular organization have important consequences for many aspects of organismal biology. Theories in ecology, evolution, and development are often based on unitary and, mainly, strictly sexually reproducing organisms, and though colonial animals dominate many marine ecosystems and habitats, recognized concepts for the study of clonal species are often lacking. In this review, we present an overview of the study of colonial and clonal animals, from the historic interests in this subject to modern research in a range of topics, including immunology, stem cell biology, aging, biogeography, and ecology. We attempt to portray the fundamental questions lying behind the biology of colonial animals, focusing on how colonial animals challenge several dogmas in biology as well as the remaining puzzles still to be answered, of which there are many.