In this paper, we provide a conceptual framework of the central aspects of mathematical definitions discussed in the mathematics education literature. Based on a systematic literature review, we found that characterizations of definitions in the mathematics education literature can be classified into five main themes: requirements, preferred features, role and function, nature, and types of definition. Within each theme, a refined set of aspects was found by means of inductive coding. We discuss each aspect and point out areas where we believe further research is needed. The framework can be used both as a research tool and a didactical tool, as it highlights many aspects of mathematical definitions that call for attention by teachers and researchers.