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The vast proliferation of sensor devices and Internet of Things enables the applications of sensor-based activity recognition. However, there exist substantial challenges that could influence the performance of the recognition system in practical scenarios. Recently, as deep learning has demonstrated its effectiveness in many areas, plenty of deep methods have been investigated to address the challenges in activity recognition. In this study, we present a survey of the state-of-the-art deep learning methods for sensor-based human activity recognition. We first introduce the multi-modality of the sensory data and provide information for public datasets that can be used for evaluation in different challenge tasks. We then propose a new taxonomy to structure the deep methods by challenges. Challenges and challenge-related deep methods are summarized and analyzed to form an overview of the current research progress. At the end of this work, we discuss the open issues and provide some insights for future directions.