Grounding is the process by which participants in a conversation establish new common ground. This process includes not just transmission of declarative utterances, but inferential and feedback processes. This process is also of critical importance to artificial dialogue systems, which include additional challenges of more limited input recognition, ontologies and inferential abilities. In this course we will review models and uses for common ground in pragmatics and computational agent theories, and then examine a variety of proposals of how common ground can be established. These proposals include both descriptive analyses of behavior, as well as generative proposals that can be used by computational systems engaged in dialogue to decide on next moves. We will also look at multimodal grounding, and advanced topics, including multiparty grounding, incremental grounding and degrees of grounding, as well as how grounding models have been used for studying other social phenomena.