Recommender systems (RSs) now play a very important role in the online lives of people as they serve as personalized filters for users to find relevant items from an array of options. Owing to their effectiveness, RSs have been widely employed in consumer-oriented e-commerce platforms. However, despite their empirical successes, these systems still suffer from two limitations: data noise and data sparsity. In recent years, generative adversarial networks (GANs) have garnered increased interest in many fields, owing to their strong capacity to learn complex real data distributions; their abilities to enhance RSs by tackling the challenges these systems exhibit have also been demonstrated in numerous studies. In general, two lines of research have been conducted, and their common ideas can be summarized as follows: (1) for the data noise issue, adversarial perturbations and adversarial sampling-based training often serve as a solution; (2) for the data sparsity issue, data augmentation--implemented by capturing the distribution of real data under the minimax framework--is the primary coping strategy. To gain a comprehensive understanding of these research efforts, we review the corresponding studies and models, organizing them from a problem-driven perspective. More specifically, we propose a taxonomy of these models, along with their detailed descriptions and advantages. Finally, we elaborate on several open issues and current trends in GAN-based RSs.