This paper reviews the state-of-the-art on the structure and dynamics of complex networks beyond pairwise interactions. It discusses the representation of higher-order interactions, measures to characterize these systems, and models to generate synthetic structures. It also covers higher-order dynamical systems, diffusion, synchronization, spreading, and evolutionary games. The paper highlights the importance of higher-order interactions in understanding complex systems and provides an overview of empirical applications and future research directions. The paper emphasizes the need to move beyond pairwise interactions to capture the rich patterns of nonlinear interactions in complex systems. It discusses various mathematical frameworks, such as simplicial complexes and hypergraphs, to describe higher-order interactions. The paper also reviews the measures and models used to analyze these systems, and discusses the implications of higher-order topology on dynamical properties. The paper concludes with an outlook on current modeling and conceptual frontiers in the field of networks beyond pairwise interactions.This paper reviews the state-of-the-art on the structure and dynamics of complex networks beyond pairwise interactions. It discusses the representation of higher-order interactions, measures to characterize these systems, and models to generate synthetic structures. It also covers higher-order dynamical systems, diffusion, synchronization, spreading, and evolutionary games. The paper highlights the importance of higher-order interactions in understanding complex systems and provides an overview of empirical applications and future research directions. The paper emphasizes the need to move beyond pairwise interactions to capture the rich patterns of nonlinear interactions in complex systems. It discusses various mathematical frameworks, such as simplicial complexes and hypergraphs, to describe higher-order interactions. The paper also reviews the measures and models used to analyze these systems, and discusses the implications of higher-order topology on dynamical properties. The paper concludes with an outlook on current modeling and conceptual frontiers in the field of networks beyond pairwise interactions.