How to build a machine that can continuously learn from observations in its life and make accurate inference/prediction? This is one of the central questions in Artificial Intelligence. Many challenges are present, such as the difficulty of learning from infinitely many observations (data), the dynamic nature of the environments, noisy and sparse data, the intractability of posterior inference, etc. This tutorial will discuss how the Bayesian approach provides a natural and efficient answer. We will start from the basic of Bayesian models, and then the variational Bayes method for inference. Next, we will discuss how to learn a Bayesian model from an infinite sequence of data. Some challenges such as catastrophic forgetting phenomenon, concept drifts, and overfitting will be discussed.