Creativity and innovation are important 21st-century skills, and mathematicseducation contributes to the development of these skills. However, it is far from clear how we as mathematics educators should respond to the need to contribute to our students’ development of creativity and innovation. One reason is that it is not clear what relation such creative and innovative skills have to mathematics, and how we should teach them. In this paper, I review different conceptions of creativity in mathematics education and investigate what mathematical innovation and creativity “are” in the mathematical classroom. I show how different conceptions ofmathematical innovation and creativity dominate different parts of the mathematicseducation literature, and explain how these differences can be viewed as framingmathematical creativity toward different domains.