With the widespread deployment of 5G networks and the proliferation of mobile devices, mobile network operators are confronted not only with massive data growth in mobile traffic, but also with highly complex and dynamic traffic patterns. Given these challenges to network operation, cellular traffic prediction is becoming an essential network capability for ensuring quality of service and reducing costs. Accurate and timely cellular traffic prediction is essential for resource allocation, base station energy conservation, and network optimization. Recent years have seen widespread adoption of deep-learning-based models for cellular traffic prediction, with notable performance improvements. This survey encompasses representative data, model architectures, and state-of-the-art performance to provide a comprehensive account of deep learning techniques for cellular traffic prediction. After defining the problem of cellular traffic prediction and describing the available data, we describe in detail how deep learning techniques are used to capture the most crucial temporal and spatial dependencies of cellular traffic. We then summarize the state-of-the-art performance on 2 popular open datasets with multiple data settings to facilitate the comparison of deep-learning-based methods. Finally, we briefly outline the applications of cellular traffic prediction and discuss the remaining challenges and future research directions.