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The increasing amount and complexity of clinical data require an appropriate way of storing and analyzing those data. Traditional approaches use a tabular structure (relational databases) for storing data and thereby complicate storing and retrieving interlinked data from the clinical domain. Graph databases provide a great solution for this by storing data in a graph as nodes (vertices) that are connected by edges (links). The underlying graph structure can be used for the subsequent data analysis (graph learning). Graph learning consists of two parts: graph representation learning and graph analytics. Graph representation learning aims to reduce high-dimensional input graphs to low-dimensional representations. Then, graph analytics uses the obtained representations for analytical tasks like visualization, classification, link prediction and clustering which can be used to solve domain-specific problems. In this survey, we review current state-of-the-art graph database management systems, graph learning algorithms and a variety of graph applications in the clinical domain. Furthermore, we provide a comprehensive use case for a clearer understanding of complex graph learning algorithms.