Generative methods (Gen-AI) are reviewed with a particular goal of solving tasks in machine learning and Bayesian inference. Generative models require one to simulate a large training dataset and to use deep neural networks to solve a supervised learning problem. To do this, we require high-dimensional regression methods and tools for dimensionality reduction (a.k.a. feature selection). The main advantage of Gen-AI methods is their ability to be model-free and to use deep neural networks to estimate conditional densities or posterior quintiles of interest. To illustrate generative methods , we analyze the well-known Ebola data set. Finally, we conclude with directions for future research.