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Human Action Recognition (HAR) aims to understand human behavior and assign a label to each action. It has a wide range of applications, and therefore has been attracting increasing attention in the field of computer vision. Human actions can be represented using various data modalities, such as RGB, skeleton, depth, infrared, point cloud, event stream, audio, acceleration, radar, and WiFi signal, which encode different sources of useful yet distinct information and have various advantages depending on the application scenarios. Consequently, lots of existing works have attempted to investigate different types of approaches for HAR using various modalities. In this paper, we present a comprehensive survey of recent progress in deep learning methods for HAR based on the type of input data modality. Specifically, we review the current mainstream deep learning methods for single data modalities and multiple data modalities, including the fusion-based and the co-learning-based frameworks. We also present comparative results on several benchmark datasets for HAR, together with insightful observations and inspiring future research directions.