Process mining is a data analytics approach which has shown promising results in healthcare including the potential to improve better management of chronic diseases such as cardiovascular diseases (CVDs). CVDs are one of the main cause of premature death worldwide, and helping cardiologists develop a better understanding of how to improve CVD care pathways should result in better outcomes for patients. This paper describes the opportunities for process mining to support such improvements and provides a summary of process mining studies undertaken in cardiology. The initial search found 1,597 potentially relevant papers which, after following a systematic review process, identified a final set of 32 relevant studies. These studies were then analyzed across five themes: process and data types; research questions; techniques, perspective and tools; methodologies; limitations and suggested future works.