Modern evolutionary theory is both a central theory and an integrative framework of the life sciences. This is reflected in the common references to evolution in modern science education curricula and contexts. In fact, evolution is a core idea that is supposed to support biology learning by facilitating the organization of relevant knowledge. In addition, evolution can function as a pivotal link between concepts and highlight similarities in the complexity of biological concepts. However, empirical studies in many countries have for decades identified deficiencies in students' scientific understanding of evolution mainly focusing on natural selection. Clearly, there are major obstacles to learning natural selection, and we argue that to overcome them, it is essential to address explicitly the general abstract concepts that underlie the biological processes, e.g., randomness or probability. Hence, we propose a two-dimensional framework for analyzing and structuring teaching of natural selection. The first--purely biological--dimension embraces the three main principles "variation," "heredity," and "selection" structured in nine key concepts that form the core idea of natural selection. The second dimension encompasses four so-called thresholds, i.e., general abstract and/or non-perceptual concepts: "randomness," "probability," "spatial scales," and "temporal scales." We claim that both of these dimensions must be continuously considered, in tandem, when teaching evolution in order to allow development of a meaningful understanding of the process. Further, we suggest that making the thresholds tangible with the aid of appropriate kinds of visualizations will facilitate grasping of the threshold concepts, and thus, help learners to overcome the difficulties in understanding the central theory of life.