Disease trajectories model patterns of disease over time and can be mined by extracting diagnosis codes from electronic health records (EHR). Process mining provides a mature set of methods and tools that has been used to mine care pathways using event data from EHRs and could be applied to disease trajectories. This paper presents a literature review on process mining related to mining disease trajectories using EHRs. Our review identified 156 papers of potential interest but only four papers which directly applied process mining to disease trajectory modelling. These four papers are presented in detail covering data source, size, selection criteria, selections of the process mining algorithms, trajectory definition strategies, model visualisations, and the methods of evaluation. The literature review lays the foundations for further research leveraging the established benefits of process mining for the emerging data mining of disease trajectories.