Surgical activity recognition is a fundamental step in computer-assisted interventions. This paper reviews the state-of-the-art in methods for automatic recognition of fine-grained gestures in robotic surgery focusing on recent data-driven approaches and outlines the open questions and future research directions. Methods: An article search was performed on 5 bibliographic databases with combinations of the following search terms: robotic, robot-assisted, JIGSAWS, surgery, surgical, gesture, fine-grained, surgeme, action, trajectory, segmentation, recognition, parsing. Selected articles were classified based on the level of supervision required for training and divided into different groups representing major frameworks for time series analysis and data modelling. Results: A total of 52 articles were reviewed. The research field is showing rapid expansion, with the majority of articles published in the last 4 years. Deep-learning-based temporal models with discriminative feature extraction and multi-modal data integration have demonstrated promising results on small surgical datasets. Currently, unsupervised methods perform significantly less well than the supervised approaches. Conclusion: The development of large and diverse open-source datasets of annotated demonstrations is essential for development and validation of robust solutions for surgical gesture recognition. While new strategies for discriminative feature extraction and knowledge transfer, or unsupervised and semi-supervised approaches, can mitigate the need for data and labels, they have not yet been demonstrated to achieve comparable performance. Important future research directions include detection and forecast of gesture-specific errors and anomalies. Significance: This paper is a comprehensive and structured analysis of surgical gesture recognition methods aiming to summarize the status of this rapidly evolving field.