Research on the role of grit -- defined as both perseverance and passion for long-term goals -- on human performance has been conducted for the past decade. It has been suggested that this non-cognitive factor is a better predictor of students' retention than traditional academic measures. These findings hold relevance for engineering education research but studies on this area are still scarce. This paper provides a systematic review of the current state of research on grit and its correlates in engineering higher education research. Publications were identified using three types of databases specific to engineering education; a final set of 31 relevant records was analysed by type of population, methods, research topics and main results. Most of the reviewed studies implemented quantitative methodologies to assess grit and also used one of the two versions of Duckworth's Grit scale. Key findings are that in engineering education research, both the conceptualisation of grit and research reporting procedures have been inconsistent. Such inconsistency hinders interpretation of the impact of grit in engineering education. In response, new research avenues and best practices for reporting are proffered.