The phenomenon of fake news has created a significant problem in the world, with characteristics that directly affect politics, the environment, people’s opinions, and trust in society, among many others. Over the last decade, however, many methods have been developed based on machine learning (ML) and, primarily, deep understanding of false news detection tasks using image identification, social networks, natural language processing, etc. This report survey describes key trends in studies of false news classification based on research work of the last ten years. The paper presents progressive techniques based on deep neural networks, such as RNNs, CNNs, and blended approaches, as well as traditional machine learning techniques, such as Naive Bayes and SVM. In the course of this time, we analyze the progress of studies in this area, the performance of multiple models and modeling options on various datasets, their limitations, and possible ways forward improving such capabilities as accurate detection of data in time and better data sources. As we have seen, the improvement in accuracy has yet to eliminate the need for hybrid models and multimodal techniques to enhance robustness against various types of misinformation.