Generative AI technologies have been deployed in many places, such as<br>(multimodal) large language models and vision generative models. Their<br>remarkable performance should be attributed to massive training data and<br>emergent reasoning abilities. However, the models would memorize and generate<br>sensitive, biased, or dangerous information originated from the training data<br>especially those from web crawl. New machine unlearning (MU) techniques are<br>being developed to reduce or eliminate undesirable knowledge and its effects<br>from the models, because those that were designed for traditional<br>classification tasks could not be applied for Generative AI. We offer a<br>comprehensive survey on many things about MU in Generative AI, such as a new<br>problem formulation, evaluation methods, and a structured discussion on the<br>advantages and limitations of different kinds of MU techniques. It also<br>presents several critical challenges and promising directions in MU research. A<br>curated list of readings can be found:<br>https://github.com/franciscoliu/GenAI-MU-Reading.