Financial fraud has a big impact on the financial sector, governments, companies and ordinary consumers. With reliance on new technologies such as cloud and mobile computing, the impact of this problem has become very dangerous. The overall losses caused by financial fraud are uncountable, which makes its detection indispensable to prevent the devastating consequences of fraud. MCDM methods are proposed as a solution of financial fraud detection (FFD) problems. The main objective of this paper is to introduce the types of financial fraud, to discover what challenges need to be solved to reduce losses and to present a state-of-the-art of the MCDM approaches dedicated to FFD that allow evaluation and selection of FFD models.