Eukaryogenesis is widely viewed as an improbable evolutionary transition uniquely affecting the evolution of life on this planet. However, scientific and popular rhetoric extolling this event as a singularity lacks rigorous evidential and statistical support. Here, we question several of the usual claims about the specialness of eukaryogenesis, focusing on both eukaryogenesis as a process and its outcome, the eukaryotic cell. We argue in favor of four ideas. First, the criteria by which we judge eukaryogenesis to have required a genuinely unlikely series of events 2 billion years in the making are being eroded by discoveries that fill in the gaps of the prokaryote:eukaryote discontinuity. Second, eukaryogenesis confronts evolutionary theory in ways not different from other evolutionary transitions in individuality; parallel systems can be found at several hierarchical levels. Third, identifying which of several complex cellular features confer on eukaryotes a putative richer evolutionary potential remains an area of speculation: various keys to success have been proposed and rejected over the five-decade history of research in this area. Fourth, and perhaps most importantly, it is difficult and may be impossible to eliminate eukaryocentric bias from the measures by which eukaryotes as a whole are judged to have achieved greater success than prokaryotes as a whole. Overall, we question whether premises of existing theories about the uniqueness of eukaryogenesis and the greater evolutionary potential of eukaryotes have been objectively formulated and whether, despite widespread acceptance that eukaryogenesis was special, any such notion has more than rhetorical value.