Introduction: Currently, the recognition of gestures and sign languages is one of the most intensively developing areas in computer vision and applied linguistics. The results of current investigations are applied in a wide range of areas, from sign language translation to gesture-based interfaces. In that regard, various systems and methods for the analysis of gestural data are being developed. Purpose: A detailed review of methods and a comparative analysis of current approaches in automatic recognition of gestures and sign languages. Results: The main gesture recognition problems are the following: detection of articulators (mainly hands), pose estimation and segmentation of gestures in the flow of speech. The authors conclude that the use of two-stream convolutional and recurrent neural network architectures is generally promising for efficient extraction and processing of spatial and temporal features, thus solving the problem of dynamic gestures and coarticulations. This solution, however, heavily depends on the quality and availability of data sets. Practical relevance: This review can be considered a contribution to the study of rapidly developing sign language recognition, irrespective to particular natural sign languages. The results of the work can be used in the development of software systems for automatic gesture and sign language recognition.