Objectives: Development of accurate auditory attention decoding (AAD) algorithms, capable of identifying the attended sound source from the speech evoked electroencephalography (EEG) responses, could lead to new solutions for hearing impaired listeners: neuro-steered hearing aids. Many of the existing AAD algorithms are either inaccurate or very slow. Therefore, there is a need to develop new EEG-based AAD methods. The first objective of this project was to investigate deep neural network (DNN) models for AAD and compare them to the state-of-the-art linear models. The second objective was to investigate whether generative adversarial networks (GANs) could be used for speech-evoked EEGdata augmentation to improve the AAD performance. Design: The proposed methods were tested in a dataset of 34 participants who performed an auditory attention task. They were instructed to attend to one of the two talkers in the front and ignore the talker on the other side and back-ground noise behind them, while high density EEG was recorded. Main Results: The linear models had an average attended vs ignored speech classification accuracy of 95.87% and 50% for ∼30 second and 8 seconds long time windows, respectively. A DNN model designed for AAD resulted in an average classification accuracy of 82.32% and 58.03% for ∼30 second and 8 seconds long time windows, respectively, when trained only on the real EEG data. The results show that GANs generated relatively realistic speech-evoked EEG signals. A DNN trained with GAN-generated data resulted in an average accuracy 90.25% for 8 seconds long time windows. On shorter trials the GAN-generated EEG data have shown to significantly improve classification performances, when compared to models only trained on real EEG data. Conclusion: The results suggest that DNN models can outperform linear models in AAD tasks, and that GAN-based EEG data augmentation can be used to further improve DNN performance. These results extend prior work and brings us closer to the use of EEG for decoding auditory attention in next-generation neuro-steered hearing aids.