Artificial Intelligence applications gradually move outside the safe walls of research labs and invade our daily lives. This is also true for Machine Learning methods on Knowledge Graphs, which has led to a steady increase in their application since the beginning of the 21st century. However, in many applications, users require an explanation of the Artificial Intelligences decision. This led to increased demand for Comprehensible Artificial Intelligence. Knowledge Graphs epitomize fertile soil for Comprehensible Artificial Intelligence, due to their ability to display connected data, i.e. knowledge, in a human- as well as machine-readable way. This survey gives a short history to Comprehensible Artificial Intelligence on Knowledge Graphs. Furthermore, we contribute by arguing that the concept Explainable Artificial Intelligence is overloaded and overlapping with Interpretable Machine Learning. By introducing the parent concept Comprehensible Artificial Intelligence, we provide a clear-cut distinction of both concepts while accounting for their similarities. Thus, we provide in this survey a case for Comprehensible Artificial Intelligence on Knowledge Graphs consisting of Interpretable Machine Learning on Knowledge Graphs and Explainable Artificial Intelligence on Knowledge Graphs. This leads to the introduction of a novel taxonomy for Comprehensible Artificial Intelligence on Knowledge Graphs. In addition, a comprehensive overview of the research on Comprehensible Artificial Intelligence on Knowledge Graphs is presented and put into the context of the taxonomy. Finally, research gaps in the field of Comprehensible Artificial Intelligence on Knowledge Graphs are identified for future research.