Healthcare professionals have long envisioned using the enormous processing powers of computers to discover new facts and medical knowledge locked inside electronic health records. These vast medical archives contain time-resolved information about medical visits, tests and procedures, as well as outcomes, which together form individual patient journeys. By assessing the similarities among these journeys, it is possible to uncover clusters of common disease trajectories with shared health outcomes. The assignment of patient journeys to specific clusters may in turn serve as the basis for personalized outcome prediction and treatment selection. This procedure is a non-trivial computational problem, as it requires the comparison of patient data with multi-dimensional and multi-modal features that are captured at different times and resolutions. In this review, we provide a comprehensive overview of the tools and methods that are used in patient similarity analysis with longitudinal data and discuss its potential for improving clinical decision making.