In this chapter, we derive and analyse models for consensus dynamics on hypergraphs. As we discuss, unless there are nonlinear node interaction functions, it is always possible to rewrite the system in terms of a new network of effective pairwise node interactions, regardless of the initially underlying multi-way interaction structure. We thus focus on dynamics based on a certain class of non-linear interaction functions, which can model different sociological phenomena such as peer pressure and stubbornness. Unlike for linear consensus dynamics on networks, we show how our nonlinear model dynamics can cause shifts away from the average system state. We examine how these shifts are influenced by the distribution of the initial states, the underlying hypergraph structure and different forms of non-linear scaling of the node interaction function.