Curiosity has long been recognized as a key factor supporting effective learning, yet its role in mathematical modelling remains underexplored. This chapter introduces a theoretical conceptualization of curiosity in the context of mathematical modelling, bridging insights from control-value theory (CVT) with the unique demands of modelling tasks. Although researchers have investigated creativity in mathematical modelling, curiosity—an epistemic emotion essential for driving enquiry and persistence—has received less attention. In this chapter, we review the relevant literature on curiosity in mathematics education, CVT, and epistemic emotions in academic settings, as well as mathematical modelling competencies and associated learning strategies. Drawing upon Muis et al.’s (Contemp Educ Psychol 42:172–185, 2015) work on emotions related to complex problem-solving, we argue that curiosity, particularly when fostered through modelling-specific strategies, is vital for the successful navigation of modelling cycles. By connecting curiosity to mathematical modelling competencies, this conceptualization provides a foundation for future research and practical application, advancing the understanding of curiosity’s function in mathematical education and suggesting pathways for its promotion.