Mathematical modelling is essential for teaching and learning of mathematics aimed at improving students’ competence in solving real-world problems with mathematical means. Innovative technology-rich approaches can provide new paradigms for mathematical modelling education, which may produce new opportunities for the learning and teaching of mathematical modelling. On the other hand, there may be a few challenges to the successful use of technology in modelling. Although several studies have focused on the use of digital technologies in modelling education, there is a lack of research on the educational potential of digital technologies in mathematical modelling. To close this research gap, we decided to conduct a descriptive systematic literature review on the advantages and challenges of using digital technologies for learners and instructors in mathematical modelling. The literature on mathematical modelling education was searched via three recognized databases. Literature search revealed 38 papers that were eligible for analysis. Based on empirical evidence, this paper describes the educational opportunities offered by digital technologies (e.g., academic, emotional/psychological, cognitive, social, and instructional/pedagogical enhancements) and challenges to their effectiveness (e.g., learners’ and instructors’ lack of competence or experience in using technology and “black-box” threats). The results of the study reveal that the advantages of the use of digital technologies in the modelling process outweigh the emerging challenges, which is a promising result discussed in detail.