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It is extremely important for companies operating in a country both to maintain their own existence and to provide benefits to the country's economy. The globalization of world economies and the resulting economic crises in the world negatively affect the economies of the states and the businesses operating in the world. Within the framework of all these situations, it has become imperative for businesses to be managed financially well and to take the necessary measures before failure in order to prevent or minimize the impact of these crises. For this reason, prediction of financial failure is important. In this study, Altman Z-Score, which is one of the first studies of traditional methods in predicting financial failure and is still frequently used in failure and bankruptcy prediction today, and traditional and modern methods such as artificial neural networks, random forest method, support vector machines, decision trees from machine learning methods are compared and explained. This study is derived from the PhD thesis written by Safak Sönmez Soydas (Advisor: Assoc. Dr. Handan ÇAM) in 2021 and accepted by Gümüshane University Graduate Education Institute.