Dialogue systems, commonly known as chatbots, have gained escalating popularity in recent times due to their wide-spread applications in carrying out chit-chat conversations with users and task-oriented dialogues to accomplish various user tasks. Existing chatbots are usually trained from pre-collected and manually-labeled data and/or written with handcrafted rules. Many also use manually-compiled knowledge bases (KBs). Their ability to understand natural language is still limited, and they tend to produce many errors resulting in poor user satisfaction. Typically, they need to be constantly improved by engineers with more labeled data and more manually compiled knowledge. This book introduces the new paradigm of lifelong learning dialogue systems to endow chatbots the ability to learn continually by themselves through their own self-initiated interactions with their users and working environments to improve themselves. As the systems chat more and more with users or learn more and more from external sources, they become more and more knowledgeable and better and better at conversing. The book presents the latest developments and techniques for building such continual learning dialogue systems that continuously learn new language expressions and lexical and factual knowledge during conversation from users and off conversation from external sources, acquire new training examples during conversation, and learn conversational skills. Apart from these general topics, existing works on continual learning of some specific aspects of dialogue systems are also surveyed. The book concludes with a discussion of open challenges for future research.