Due to the rapid development of process mining technology, the variety of process mining algorithms has increased rapidly, and the introduction of existing algorithm research articles is no longer comprehensive. In view of this, we systematically analyze and summarize process mining algorithms so far. Firstly, we analyze the current situation of process mining algorithms in general and then classify them into two categories according to their characteristics: traditional process mining algorithms and process mining algorithms based on computational intelligence and machine learning technologies. Meanwhile, we briefly introduce the basic ideas and related steps of each subclass of representative algorithms and discuss the current advantages and disadvantages of the algorithms. Finally, suggestions regarding algorithm research and improvement in the next step are proposed. The classification and summary of algorithms can help beginners to sort out relevant algorithm knowledge in the field of process mining, and the analysis of the development status and algorithm comparison can guide researchers in areas that need to be broken through.