Generative artificial intelligence aims at learning data distributions from samples, enabling it to generate new samples that are distinct yet resemble the original data distributions. Prominent methodologies include variational autoencoders, generative adversarial networks, diffusion models, and transformers, all of which are covered in detail in this chapter. Furthermore, their usage is explored in the context of computational mechanics, focusing on applications such as dimensionality reduction, data synthesis for microstructures, and anomaly detection. By providing practical examples, the chapter demonstrates how these methods can transform traditional workflows in engineering and simulation.