This review article explores the dynamics of contagion processes on higher-order networks, which are networks where interactions can involve more than two individuals. The authors highlight the importance of understanding these processes in the context of social and epidemiological systems, such as the spread of diseases, information, and behaviors. They discuss the limitations of traditional pairwise interaction models and introduce higher-order interactions using hypergraphs, which can capture group dynamics and complex influence mechanisms. The article presents a unified formalism for various contagion models, including the SIS and SIR models, and demonstrates how these models can be reduced to classical pairwise models. It also reviews different analytical approaches to studying these models, such as mean-field theory, heterogeneous mean-field theory, and facet approximation. The authors analyze the behavior of these models, noting phenomena like discontinuous transitions, bistability, and multistability, and discuss the impact of structural heterogeneity and temporal dynamics. The review concludes with a discussion of open questions and future research directions, emphasizing the need for further theoretical and empirical work to understand the complex dynamics of contagion processes on higher-order networks. The authors suggest that higher-order models can provide richer and more realistic representations of social and epidemiological phenomena, but more research is needed to fully characterize their properties and mechanisms.This review article explores the dynamics of contagion processes on higher-order networks, which are networks where interactions can involve more than two individuals. The authors highlight the importance of understanding these processes in the context of social and epidemiological systems, such as the spread of diseases, information, and behaviors. They discuss the limitations of traditional pairwise interaction models and introduce higher-order interactions using hypergraphs, which can capture group dynamics and complex influence mechanisms. The article presents a unified formalism for various contagion models, including the SIS and SIR models, and demonstrates how these models can be reduced to classical pairwise models. It also reviews different analytical approaches to studying these models, such as mean-field theory, heterogeneous mean-field theory, and facet approximation. The authors analyze the behavior of these models, noting phenomena like discontinuous transitions, bistability, and multistability, and discuss the impact of structural heterogeneity and temporal dynamics. The review concludes with a discussion of open questions and future research directions, emphasizing the need for further theoretical and empirical work to understand the complex dynamics of contagion processes on higher-order networks. The authors suggest that higher-order models can provide richer and more realistic representations of social and epidemiological phenomena, but more research is needed to fully characterize their properties and mechanisms.