After nearly fifty years of theoretical exploration, this chapter undertakes a comparative analysis of various approaches to the analysis of trends and periods across Big History. The identified approaches include the Self-organizing Universe (Jantsch), Grand Unified Narrative (Christian), Cosmic Evolution (Chaisson), Perasmology (Aunger), Extended Evolution (LePoire), the Grand Sequence (Henriques and Volk) and Mega Evolution (Grinin). Each approach is evaluated based on scientific criteria such as parsimony, testability, external validity and the identification of natural kinds. Each approach has strengths and weaknesses, but looking overall, there is a disappointing lack of progress and the absence of a clear theoretical core, which suggests that the field is still grappling with fundamental challenges. Points of convergence do emerge, however: agreement among scholars that the overarching trend in Big History is an increase in maximal complexity across the various spatial and temporal scales since the origin of the universe; that a single, unified theory encompassing the physical, chemical/geological, biological, and cultural eras of Big History is feasible; of the need for a hierarchical treatment of periods within eras, each of which has specific dynamics; on the idea that significant changes, such as shifts in energy flow density or reaching system capacity, create conditions that initiate transitions to new periods and eras; and that transitions are themselves complex processes involving changes in energy flow, information and structural organization. However, disagreement persists concerning the best theory to explain these phenomena and which periods should be canonical in defining the Big History narrative. The chapter suggests potential avenues for advancement, including collaborative efforts to reach consensus, the use of Big History as the overarching frame for general education and the need for empirical studies to demonstrate the utility of Big Historical perspectives. Despite the obstacles, the chapter emphasizes the ongoing potential of Big History as a discipline, provided a concerted effort is made to address theoretical gaps and establish common ground.
