This monograph is the first survey of neural approaches to conversational AI that targets Natural Language Processing and Information Retrieval audiences. It provides a comprehensive survey of the neural approaches to conversational AI that have been developed in the last few years, covering QA, task-oriented and social bots with a unified view of optimal decision making. The authors draw connections between modern neural approaches and traditional approaches, allowing readers to better understand why and how the research has evolved and to shed light on how they can move forward. They also present state-of-the-art approaches to training dialogue agents using both supervised and reinforcement learning. Finally, the authors sketch out the landscape of conversational systems developed in the research community and released in industry, demonstrating via case studies the progress that has been made and the challenges that are still being faced. Neural Approaches to Conversational AI is a valuable resource for students, researchers, and software developers. It provides a unified view, as well as a detailed presentation of the important ideas and insights needed to understand and create modern dialogue agents that will be instrumental to making world knowledge and services accessible to millions of users in ways that seem natural and intuitive.