The establishment and maintenance of common ground, i.e. mutual knowledge, beliefs and assumptions, is important for dialogue systems in order to be seen as valid interlocutors in both task-oriented and open-domain dialogue. It is therefore important to provide these systems with knowledge models, so that their conversations could be grounded in the knowledge about the relevant domain. Additionally, in order to facilitate understanding, dialogue systems should be able to track the knowledge

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... t the beliefs of the user and the level of their knowledgeability, e.g., the assumptions that they hold or the extent to which a piece of knowledge has been accepted by the user and can now be considered shared. This article provides a basic overview of current research on knowledge modelling for the establishment of common ground in dialogue systems. The presented body of research is structured along three types of knowledge that can be integrated into the system: (1) factual knowledge about the world, (2) personalised knowledge about the user, (3) knowledge about user's knowledge and beliefs. Additionally, this article discusses the presented body of research with regards to its relevance for the current state-of-the-art dialogue systems and several ideal application scenarios that future research on knowledge modelling for common ground establishment could aim for.