Mathematical flexibility has been widely acknowledged as an important learning goal in mathematical education and has received increasing research attention in order to explore its nature, facilitating mechanisms, and promotion interventions. Given that researchers conceptualize, assess, and explain flexibility in mathematical problem solving from different perspectives, a systematic review could contribute to an integrated framework of mathematical flexibility. To this end, we review mathematical flexibility in terms of its concepts, measurements, and related research on influencing factors and effective interventions. Additionally, we propose a three-dimensional model focusing on analytic units, manifestation forms, and evaluation criteria, which we argue advances a comprehensive understanding of mathematical flexibility. Overall, this review not only helps to reveal the multifaceted construct of mathematical flexibility in theory but also provides supporting evidence for targeted educational interventions in teaching practice. In addition, we discuss each aspect of mathematical flexibility and propose future research directions to potentially broaden and deepen mathematical flexibility research.