Emotion recognition has been used in a wide range of different fields, such as human–computer interaction, safe driving, education and medical treatment. Compared with text, speech, expression and other physiological signals, electroencephalogram (EEG) signals can reflect an individual's emotion states more directly, objectively and accurately, and are less affected by the individual’s subjective consciousness. Following the continuous progress of EEG acquisition equipment over recent years, the acquisition of EEG signals has become increasingly convenient. Emotion recognition based on EEG signals has attracted more and more interest from a wide variety of researchers. This paper first reviews the basic theory of emotion recognition, including discrete and continuous emotion models, the development of acquisition equipment and the internal relationship between EEG signals and emotion recognition. A review of the application of deep learning algorithms to EEG emotion recognition is then presented, with a focus on the extraction of deep EEG features and emotion recognition by single deep learning models, attention-based deep learning models, hybrid deep learning models and domain adaptation-based deep learning models. Taking the public datasets SEED, DEAP, SEED-IV, DREAMER and MPED as examples, representative methods of subject-dependent and subject-independent experiments are quantitatively compared and analysed, and the significance of subject-independent research is indicated. Finally, aiming at the problems of dataset's application limitations, model optimisation and subject variability in existing research, the possible solutions to the corresponding problems are summarised, and the future development trends and prospects are proposed.