This chapter presents a theoretical approach to the study of anthropogenesis as a middle way between empirical research and abstract constructions. Reconstructions of past phenomena and processes must be based on a conceptual understanding that the collection of new data alone cannot provide. The unity of the approach is based on the general logic of explanation through generalization and combination of known evolutionary principles, regularities, and mechanisms. This chapter presents a list of key problems whose conceptual solutions should guide the explanation of individual phenomena and processes of anthropogenesis. The principle of provisioning is formulated: in the presence of an acute unsatisfied need or concern in the surviving part of the population, a structure providing this need or concern must necessarily emerge by various attempts and ingredients. Author presents a method of reconstructing hominin behavioral and psychological development from indirect data. Karl Hempel’s extended nomological scheme is used to explain the emergence of new structures. This work proposes the approach of extended evolutionary synthesis, based on a critique of neo-Darwinism (synthetic theory of evolution). The approach includes the concepts of gene-culture coevolution, cultural drive, epigenetics, multi-level selection, niche construction, and the Baldwin effect, which brings the approach closer to neo-Lamarckism. The approach highlights levels of evolution (macro to micro), levels of selection, and the systemic principle of “outside-in” causality. The concept of coevolution of concerns and structures complements the approach as a spiral development, in which each cycle leads to new challenges-threats and challenges-opportunities, corresponding to the superstructure of new structures and new concerns. The chapter highlights particularly flexible and multifunctional structures, metaphorically called “magic wands,” and shows their role in the evolution of some species of higher mammals, including primates.