Generative adversarial networks (GANs) are a novel framework for training generative models in an adversarial setup. This paper provides a comprehensive review of recent developments in GANs, including their basic theory, training mechanisms, latent space, and various variants. The paper discusses the instability and convergence issues in GANs from the perspectives of statistics, game theory, and control theory, and presents techniques for stable training. It also addresses the challenges in evaluating GANs, as there is no consensus on suitable evaluation metrics. The paper conducts experiments to compare representative GAN variants based on these metrics and discusses their applications. Finally, it outlines important open issues and future research trends in GANs. Generative models are widely used in artificial intelligence and machine learning for generating high-quality images. Deep generative models, such as deep belief networks, deep Boltzmann machines, and restricted Boltzmann machines, use maximum likelihood to estimate data distributions. However, these models often produce poor samples and require numerous approximations due to intractable computations. Alternative methods, such as contrastive divergence, score matching, and noise-contrastive estimation, have been proposed to address these issues. However, these methods face challenges in computational efficiency and statistical accuracy. GANs are a newly emerging framework in generative models. Unlike NCE, which uses the same value function as GANs, GANs incorporate a separate discriminative model in addition to the generative model. The generator and discriminator are trained simultaneously in a zero-sum game, where the generator aims to generate realistic images to fool the discriminator. Despite their potential, GANs are known to be highly unstable to train, and there is a lack of understanding of how they converge. The paper discusses the sources of instability and convergence issues in GANs and presents techniques for their stable training. It also addresses the challenges in evaluating GANs and discusses their applications. Finally, it outlines important open issues and future research trends in GANs.Generative adversarial networks (GANs) are a novel framework for training generative models in an adversarial setup. This paper provides a comprehensive review of recent developments in GANs, including their basic theory, training mechanisms, latent space, and various variants. The paper discusses the instability and convergence issues in GANs from the perspectives of statistics, game theory, and control theory, and presents techniques for stable training. It also addresses the challenges in evaluating GANs, as there is no consensus on suitable evaluation metrics. The paper conducts experiments to compare representative GAN variants based on these metrics and discusses their applications. Finally, it outlines important open issues and future research trends in GANs. Generative models are widely used in artificial intelligence and machine learning for generating high-quality images. Deep generative models, such as deep belief networks, deep Boltzmann machines, and restricted Boltzmann machines, use maximum likelihood to estimate data distributions. However, these models often produce poor samples and require numerous approximations due to intractable computations. Alternative methods, such as contrastive divergence, score matching, and noise-contrastive estimation, have been proposed to address these issues. However, these methods face challenges in computational efficiency and statistical accuracy. GANs are a newly emerging framework in generative models. Unlike NCE, which uses the same value function as GANs, GANs incorporate a separate discriminative model in addition to the generative model. The generator and discriminator are trained simultaneously in a zero-sum game, where the generator aims to generate realistic images to fool the discriminator. Despite their potential, GANs are known to be highly unstable to train, and there is a lack of understanding of how they converge. The paper discusses the sources of instability and convergence issues in GANs and presents techniques for their stable training. It also addresses the challenges in evaluating GANs and discusses their applications. Finally, it outlines important open issues and future research trends in GANs.