 For roughly 100 years after Darwin’s Origin, phylogenetic research in biology was common and important. Yet, phylogenetics proceeded without much in the way of underlying theory or explicable methodology—rather, the systematist with extensive knowledge of some group simply relied on their judgment as to which character traits looked genuinely homologous and which character transformations seemed plausible. Some phylogenies were widely agreed upon due to the fact that when homologies are clear, inference is easy. As early as the late 1800s, there was a general consensus among systematists around the branching order of many of the groups presented in  Figure 1.  However, the relative placement of the coelacanth and lungfish was disputed almost immediately upon discovery of the former in 1938 (Thomson 1991)—a dispute that has continued to draw attention from biologists (e.g., Bockmann, De Carvalho, &amp; De Carvalho 2013; Amemiya et al. 2013; Takezaki &amp; Nishihara 2017).