Human group activity recognition (GAR) has attracted significant attention from computer vision researchers due to its wide practical applications in security surveillance, social role understanding and sports video analysis. In this paper, we give a comprehensive overview of the advances in group activity recognition in videos during the past 20 years. First, we provide a summary and comparison of 11 GAR video datasets in this field. Second, we survey the group activity recognition methods, including those based on handcrafted features and those based on deep learning networks. For better understanding of the pros and cons of these methods, we compare various models from the past to the present. Finally, we outline several challenging issues and possible directions for future research. From this comprehensive literature review, readers can obtain an overview of progress in group activity recognition for future studies.