Context. Electroencephalography (EEG) is a complex signal and can require several years of training, as well as advanced signal processing and feature extraction methodologies to be correctly interpreted. Recently, deep learning (DL) has shown great promise in helping make sense of EEG signals due to its capacity to learn good feature representations from raw data. Whether DL truly presents advantages as compared to more traditional EEG processing approaches, however, remains an open question.Objective. In this work, we review 156 papers that apply DL to EEG, published between January 2010 and July 2018, and spanning different application domains such as epilepsy, sleep, braincomputer interfacing, and cognitive and affective monitoring. We extract trends and highlight interesting approaches from this large body of literature in order to inform future research and formulate recommendations.Methods. Major databases spanning the fields of science and engineering were queried to identify relevant studies published in scientific journals, conferences, and electronic preprint repositories. Various data items were extracted for each study pertaining to 1) the data, 2) the preprocessing methodology, 3) the DL design choices, 4) the results, and 5) the reproducibility of the experiments. These items were then analyzed one by one to uncover trends. * The first two authors contributed equally to this work.Significance. To help the community progress and share work more effectively, we provide a list of recommendations for future studies. We also make our summary table of DL and EEG papers available and invite authors of published work to contribute to it directly.