Over the last 20 years, networks have emerged as a powerful paradigm to model complex systems. Despite its many successes, the abstraction of a system in terms of nodes and edges has also some fundamental modelling limitations, that have become more apparent with the increasing availability of multi-way relational data recently. Within the emerging field of higher-order networks, researchers have tested the limits of the network paradigm, and proposed extensions with richer interactions, including multiplex networks, higher-order Markov models and multiway networks. In this talk, I will start by providing an overview of recent results on higher-order networks, before turning to multiway networks and focusing on the problem of non-linear consensus on hypergraphs.