  Network science has evolved into an indispensable platform for studying
complex systems. But recent research has identified limits of classical
networks, where links connect pairs of nodes, to comprehensively describe group
interactions. Higher-order networks, where a link can connect more than two
nodes, have therefore emerged as a new frontier in network science. Since group
interactions are common in social, biological, and technological systems,
higher-order networks have recently led to important new discoveries across
many fields of research. We here review these works, focusing in particular on
the novel aspects of the dynamics that emerges on higher-order networks. We
cover a variety of dynamical processes that have thus far been studied,
including different synchronization phenomena, contagion processes, the
evolution of cooperation, and consensus formation. We also outline open
challenges and promising directions for future research.
