Evolution has led to a great diversity that ranges from elegant simplicity to ornate complexity. Many complex features are often assumed to be more functional or adaptive than their simpler alternatives. However, in 1999, Arlin Stolzfus published a paper in the Journal of Molecular Evolution that outlined a framework in which complexity can arise through a series of non-adaptive steps. He called this framework Constructive Neutral Evolution (CNE). Despite its two-decade-old roots, many evolutionary biologists still appear to be unaware of this explanatory framework for the origins of complexity. In this per- spective piece, we explain the theory of CNE and how it changes the order of events in narratives that describe the evolution of complexity. We also provide an extensive list of cellular features that may have become more complex through CNE. We end by discussing strategies to determine whether complexity arose through neutral or adaptive processes.