Recent years have witnessed the rapid growth and adoption of generative AI in diverse industries such as healthcare, retail, financial services, and more. In the midst of these advancements, there are also rising concerns about misinformation, disinformation, and other ethical issues surrounding generative AI. Towards addressing these concerns, a variety of countermeasures are being developed. In this survey paper, we provide a comprehensive overview of various research methods and best practices to detect and mitigate misinformation and disinformation associated with generative AI, in particular large language models (LLMs). Specifically, we provide a holistic summary of related datasets and benchmarks, detection and mitigation methods, review human-centric best practices and guidelines suggested towards addressing these challenges, and outline open problems and future directions. We hope that the survey will help researchers and practitioners understand the latest advances at the intersection of generative AI and misinformation/disinformation.