This paper presents a comprehensive review of modern recommender systems (RS) using generative models (Gen-RecSys). The authors highlight key advancements in RS using generative models, including interaction-driven generative models, the use of large language models (LLMs) and textual data for natural language recommendation, and the integration of multimodal models for generating and processing images/videos in RS. The survey also identifies open challenges and discusses necessary paradigms for evaluating the impact and harm of Gen-RecSys. The paper accompanies a tutorial presented at ACM KDD'24 and provides supporting materials at: https://encr.pw/vDhLq. The paper discusses various generative models used in RS, including auto-encoding models, auto-regressive models, generative adversarial networks (GANs), and diffusion models. It also explores the use of LLMs in recommendation tasks, including zero- and few-shot learning, fine-tuning, retrieval-augmented generation (RAG), and feature extraction for downstream recommendation. The paper also covers multimodal approaches, which jointly use multiple data types such as text, image, and video to enhance and improve the recommendation experience. The paper also discusses the evaluation of Gen-RecSys, including offline impact, online and longitudinal evaluations, conversational evaluation, and evaluating for societal impact. It highlights key evaluation challenges, addressing performance, fairness, privacy, and societal impact, thereby establishing a new benchmark for future research in the domain. The paper concludes with a discussion of future directions for Gen-RecSys, including RAG, tool-augmented LLMs for conversational recommendation, personalized content generation, and red-teaming.This paper presents a comprehensive review of modern recommender systems (RS) using generative models (Gen-RecSys). The authors highlight key advancements in RS using generative models, including interaction-driven generative models, the use of large language models (LLMs) and textual data for natural language recommendation, and the integration of multimodal models for generating and processing images/videos in RS. The survey also identifies open challenges and discusses necessary paradigms for evaluating the impact and harm of Gen-RecSys. The paper accompanies a tutorial presented at ACM KDD'24 and provides supporting materials at: https://encr.pw/vDhLq. The paper discusses various generative models used in RS, including auto-encoding models, auto-regressive models, generative adversarial networks (GANs), and diffusion models. It also explores the use of LLMs in recommendation tasks, including zero- and few-shot learning, fine-tuning, retrieval-augmented generation (RAG), and feature extraction for downstream recommendation. The paper also covers multimodal approaches, which jointly use multiple data types such as text, image, and video to enhance and improve the recommendation experience. The paper also discusses the evaluation of Gen-RecSys, including offline impact, online and longitudinal evaluations, conversational evaluation, and evaluating for societal impact. It highlights key evaluation challenges, addressing performance, fairness, privacy, and societal impact, thereby establishing a new benchmark for future research in the domain. The paper concludes with a discussion of future directions for Gen-RecSys, including RAG, tool-augmented LLMs for conversational recommendation, personalized content generation, and red-teaming.