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The diversity of the research in the field of Calculus education makes it difficult to produce an exhaustive state-of-the-art summary. We therefore focus on the main trends in the field in order to detect punctual evolutions that permit us to go beyond this survey and to put forward new research questions. The research results, in spite of their variety, revealed a cornerstone issue that is strongly linked to the formalism of Calculus concepts and to the difficulties it generates in the learning and teaching process. This formalism supports the mathematical existence of Calculus concepts; the first step in the teaching of Calculus is to contextualize such existence. In this spirit, the research highlights the complexity required to cope with two problematic situations: (1) the actual gap between students’ prior knowledge and the mathematical foundation of Calculus concepts; (2) the ultimate reliance of Calculus on formal definitions and proofs.