Mathematical creativity as a key ability in our increasingly automated and interconnected, high-technology based society and economy is increasingly in the focus of mathematics education research. The recent scientific discussion in this domain is shifting from a product view, on written solutions and drawings, to a process view, which aims to investigate the different stages of how students come up with creative ideas. The latter is, however, a challenge. In this theoretical-methodological paper, we present and discuss the opportunities that eye-tracking offers for studying creativity in a process view. We discuss in which way eye-tracking allows to obtain novel answers to the questions of how original ideas come up, how they evolve and what leads to the so-called Eureka!-moment. We focus on video-based eye tracking approaches, discuss pros and cons of screen-based and mobile eye tracking, and illustrate methods of data analysis and their benefits for research on mathematical creativity.