Developing an intelligent dialogue system that not only emulates human conversation, but also can answer questions of topics ranging from latest news of a movie star to Einstein's theory of relativity, and fulfill complex tasks such as travel planning, has been one of the longest running goals in AI. The goal has remained elusive until recently. We are now observing promising results both in academia and industry, as large amounts of conversational data become available for training, and the breakthroughs in deep learning (DL) and reinforcement learning (RL) are applied to conversational AI. In this tutorial, we start with a brief introduction to the recent progress on DL and RL that is related to conversational AI. Then, we describe in detail the state-of-the-art neural approaches developed for three types of dialogue systems, or bots. The first is a question answering (QA) bot. Equipped with rich knowledge drawn from various data sources including Web documents and pre-complied knowledge graphs (KG's), the QA bot can provide concise direct answers to user queries. The second is a task-oriented dialogue system that can help users accomplish tasks ranging from meeting scheduling to vacation planning. The third is a social chat chatbot which can converse seamlessly and appropriately with humans, and often plays roles of a chat companion and a recommender.