 Revisiting the utility of idealizing away the complexity of phylogenetic histories has generated both hard challenges and new opportunities for phylogeneticists moving forward (Haber 2012, 2019; Velasco 2012). Here we provide a brief overview of what relaxing these assumptions amounts to, and what kinds of complexity we are acknowledging when these assumptions no longer hold. Following this, we briefly describe how this impacts the central commitments and project of phylogenetics.