Generative models are mathematical frameworks that are designed to generate new data that is similar to an existing dataset. These models are trained on a dataset and learn to create new examples that mirror its patterns. Popular examples include Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs). They are crucial in fields like image synthesis, text generation, and data augmentation, contrasting with discriminative models which focus on categorizing data.