Generative AI technologies have been deployed in many places, such as(multimodal) large language models and vision generative models. Theirremarkable performance should be attributed to massive training data andemergent reasoning abilities. However, the models would memorize and generatesensitive, biased, or dangerous information originated from the training dataespecially those from web crawl. New machine unlearning (MU) techniques arebeing developed to reduce or eliminate undesirable knowledge and its effectsfrom the models, because those that were designed for traditionalclassification tasks could not be applied for Generative AI. We offer acomprehensive survey on many things about MU in Generative AI, such as a newproblem formulation, evaluation methods, and a structured discussion on theadvantages and limitations of different kinds of MU techniques. It alsopresents several critical challenges and promising directions in MU research. Acurated list of readings can be found:https://github.com/franciscoliu/GenAI-MU-Reading.