Bayesian methods provide a framework for representing and manipulating uncertainty, for learning from noisy data, and for making decisions that maximize expected utility----components which are important to both AI and Machine Learning. However, although Bayesian methods have become more popular in recent years, there remains a good degree of skepticism with respect to taking a fully Bayesian approach. This talk will introduce fundamental topics in Bayesian statistics as they apply to machine learning and AI, and address some misconceptions about Bayesian approaches. I will then discuss some current work on non-parametric Bayesian machine learning, particularly in the area of unsupervised learning.