Embodied cognition has recently gained increasing attention in mathematics education research. However, little is known about ways to use an embodied approach to reach for mathematical abstraction. In this study, we investigate this topic for the case of functional thinking (FT) using digital technology (DT) through a systematic literature study. We searched four databases, resulting in a corpus of 51 papers. As a result, we found that action-based and perception-based embodied approaches to contextual/situational abstraction are more prevalent in literature than pseudo-embodied approaches. In addition, the covariation and correspondence views on function are more frequently addressed compared to input-output and mathematical object views. We conclude with a discussion on the interplay of embodied approaches and abstraction in FT. For future research, we suggest investigating embodied approaches using digital technology for developing FT concerning different types of mathematical abstraction.