Earthquakes are one of the most dangerous natural disasters, primarily due to the fact that they often occur without an explicit warning, leaving no time to react. This fact makes the problem of earthquake prediction extremely important for the safety of humankind. Despite the continuing interest in this topic from the scientific community, there is no consensus as to whether it is possible to find the solution with sufficient accuracy. However, successful application of machine learning techniques to different fields of research indicates that it would be possible to use them to make more accurate short-term forecasts. This paper reviews recent publications where application of various machine learning based approaches to earthquake prediction was studied. The aim is to systematize the methods used and analyze the main trends in making predictions. We believe that this research will be useful and encouraging for both earthquake scientists and beginner researchers in this field.