In order to approximate the underlying process of temporal data, time series prediction has been a hot research topic for decades. Developing predictive models plays an important role in interpreting complex real-world elements. With the sharp increase in the quantity and dimensionality of data, new challenges, such as extracting deep features and recognizing deep latent patterns, have emerged, demanding novel approaches and effective solutions. Deep learning, composed of multiple processing layers to learn with multiple levels of abstraction, is, now, commonly deployed for overcoming the newly arisen difficulties. This paper reviews the state-of-the-art developments in deep learning for time series prediction. Based on modeling for the perspective of conditional or joint probability, we categorize them into discriminative, generative, and hybrids models. Experiments are implemented on both benchmarks and real-world data to elaborate the performance of the representative deep learning-based prediction methods. Finally, we conclude with comments on possible future perspectives and ongoing challenges with time series prediction.