Generative Adversarial Networks (GANs) are artificial neural networks belonging to the class of implicit generative models. GANs achieved the state-of-the-art performance in most unsupervised tasks that require learning how to generate new samples which look statistically indistinguishable from those drawn by an unknown real-world distribution. The main idea behind GANs is to set up a competition between two networks: the generator and the discriminator. These models have emerged as one of the most powerful solutions for realistic image generation and their use encompasses also different applications, such as model-based reinforcement learning or semi-supervised learning. However, a comprehensive understanding of the theoretical conditions underlying the successful training of GANs is still missing.