The chapter covers the fast-changing landscape of generative AI with an in-depth presentation of the underlying principles, techniques, and applications. It will introduce the reader to the very basics of generative modelling, contrasting generative models with their discriminative versions, and give very basic ideas of probability distributions and latent spaces and the role of sampling for generating new data. It then reviews some of the most influential generative models, such as GANs, VAEs, and transformer-based models like GPT, explaining their structure, how to train them, and finally, what problems could happen while training in practice. After the theoretical introduction, some techniques involved in generative AI are presented. It deals explicitly with GANs and VAEs, focusing on their unique architectures, training methodologies, and specific challenges: namely, mode collapse and the training instability of GANs on one side, and the probabilistic modeling together with latent space exploration on the other side of VAEs. These techniques find applications in a number of domains, from image and video generation to data augmentation, anomaly detection, and synthetic data creation for a host of domains like healthcare and art. The chapter summarizes trends and ethics existing in already established models within generative AI related to problems such as bias in content generated and possible missuses of technologies. It aims to help the reader achieve a deep level of understanding about generative AI, from its theoretical underpinnings to its most modern applications and future directions. Herein presented in-depth analysis thus offers a strong foundation for those wishing to join the fast-paced development process of this highly advancing field: generative AI.