In recent years, deep learning algorithms have been developed rapidly, and they are becoming a powerful tool in biomedical engineering. Especially, there has been an increasing focus on the use of deep learning algorithms for decoding physiological or pathological status of the brain from electroencephalographic (EEG). This paper overviews current application of deep learning algorithms in various EEG decoding tasks, and introduces commonly used algorithms, typical application scenarios, important progresses and existing problems. Firstly, the basic principles of deep learning algorithms used in EEG decoding is briefly described, including convolutional neural network, deep belief network, autoencoder and recurrent neural network. In this paper, existing applications of deep learning on EEG is discussed, including brain-computer interfaces, cognitive neuroscience and diagnosis of brain disorders. Finally, this paper outlines some key problems that will be addressed in future applications of deep learning for EEG decoding, such as parameter selection, computational complexity, and the capability of generalization.