Generative models are a class of AI models capable of creating new instances of data by learning and sampling from their statistical distributions. In recent years, these models have gained prominence in machine learning due to the development of approaches such as generative adversarial networks (GANs), variational autoencoders (VAEs), and transformer-based architectures such as GPT. These models have applications across various domains, such as image generation, text synthesis, and music composition. In recommender systems, generative models, referred to as Gen-RecSys, improve the accuracy and diversity of recommendations by generating structured outputs, text-based interactions, and multimedia content. By leveraging these capabilities, Gen-RecSys can produce more personalized, engaging, and dynamic user experiences, expanding the role of AI in eCommerce, media, and beyond. Our book goes beyond existing literature by offering a comprehensive understanding of generative models and their applications, with a special focus on deep generative models (DGMs) and their classification. We introduce a taxonomy that categorizes DGMs into three types: ID-driven models, large language models (LLMs), and multimodal models. Each category addresses unique technical and architectural advancements within its respective research area. This taxonomy allows researchers to easily navigate developments in Gen-RecSys across domains such as conversational AI and multimodal content generation. Additionally, we examine the impact and potential risks of generative models, emphasizing the importance of robust evaluation frameworks.