This chapter develops the extended evolutionary approach, supplemented by the model of the coevolution of concerns and structures, in application to the problems of anthropogenesis. Individuals, groups, and populations make attempts (trials, probes) of various types and scales in response to challenges-threats and challenges-opportunities. Behavioral trials include Thorndike-Skinner random trials and Köhler’s purposive trials. Evolutionary attempts include random mutations (Dobzhansky’s trials), changes in genomes influenced by interactions between organisms and their niches and shifts in selection criteria (Lamarck-Baldwin attempts), and contenders for the role of transgenerationally transmitted cultural patterns (Kroeber’s attempts). The author distinguishes four spheres of being as “worlds” of different ontological status. The first three spheres correspond roughly to K. Popper’s “three worlds”: Biotechno-, Psycho-, and Culturosphere. The Sociosphere includes relations, rules, and institutions that Popper did not identify as a separate world. The author pays special attention to the “cultural drive” as a hominin-specific driver of evolutionary development. This chapter treats cultural patterns (language, ideas, technologies) transmitted through education and training as “magic wands” specific to anthropogenesis and human history, providing special adaptability and evolutionary flexibility. The author interprets the progressive evolutionary strategy of hominins as a cascade of aromorphoses—qualitative leaps in development that allow to go beyond the limits of previous niches. He emphasizes the importance of changes in social relations and orders as special structures, creating new types of concerns. The brain and cognitive abilities are “social tools” that develop under conditions of competition and cooperation. The chapter includes a number of general evolutionary principles that serve as a heuristic and logical basis for explaining the course of anthropogenesis: the principle of provision, the principle of spiral coevolution, the principle of directional evolution, and the principle of continuity. The author points out limitations in the use of some principles based on the analysis of counterexamples.