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Nowadays the importance of predicting the future financial situation of companies is becoming more and more important, and it is useful both for the companies themselves and for the market stakeholders because it helps in timely information provision and supporting decision-making processes, to achieve their goals and protect them from the past financial losses. The need of predicting the future financial situation of companies led researchers to deal with the development of automated predicting systems. Until today most studies have applied traditional statistical analysis and machine learning methods, but with several disadvantages due to their limited capabilities. So, the need of using more advanced technology was imperative. In the last years the technological progress and the ability to manage large amounts of data created the conditions for the development of deep learning methods. It is about an advanced machine learning approach which in fact is already used in many applications covering a wide range of scientific fields with success. The object of this paper is the bibliographic review of fifteen research articles which have taken place in recent years to predict the probability of fraud, financial distress, bankruptcy, financial failure and going concern of companies. The purpose is to assess the superiority and the effectiveness of deep learning models over traditional statistical and machine learning models, to identify the benefit of their use and also the opportunities they offer for future research. Indeed, in all the experimental procedures, the deep learning models showed excellent performance, confirming their superiority and reliability, as well as indicating that it is about a promising method capable to contribute to strengthening the decision-making processes of all stakeholders, improving and accelerating the auditing procedures and more efficient administration. However, it needs further research, given the fact that until today its application in financial analysis is still limited.