Since their introduction in 2014, generative adversarial networks (GANs) have achieved state-of-the-art performance on a wide array of machine learning tasks, outperforming standard maximum likelihood-based methods. In this seminar, we compare and contrast the GAN and maximum likelihood approaches, and provide theoretical evidence that the game-based design of GANs could contribute to a superior generalization performance from training samples to unseen data in comparison to deep maximum likelihood methods such as autoregressive and flow-based models. Furthermore, we demonstrate that the common divergence/distance measures targeted by GANs are more suitable for learning multi-modal distributions than the KL-divergence optimized by maximum likelihood learners. We discuss several numerical results supporting our theoretical comparison of the GAN and maximum likelihood frameworks.