Contagion dynamics on higher-order networks have gained attention due to their potential to model complex processes like disease spread and social influence more accurately. This review summarizes recent research on these models, highlighting their functional forms and analytical approaches. The paper discusses the transition from pairwise to higher-order interactions, emphasizing the role of hypergraphs and simplicial complexes in capturing group dynamics. It presents a unified formalism that encompasses various models, including SIS and SIR, and explores their behavior in different network structures. The study also addresses challenges in empirical validation and suggests future research directions. Key findings include the existence of critical mass thresholds, multistability, and the influence of network structure on contagion dynamics. The review underscores the importance of both theoretical and empirical approaches in advancing the understanding of higher-order contagion models.Contagion dynamics on higher-order networks have gained attention due to their potential to model complex processes like disease spread and social influence more accurately. This review summarizes recent research on these models, highlighting their functional forms and analytical approaches. The paper discusses the transition from pairwise to higher-order interactions, emphasizing the role of hypergraphs and simplicial complexes in capturing group dynamics. It presents a unified formalism that encompasses various models, including SIS and SIR, and explores their behavior in different network structures. The study also addresses challenges in empirical validation and suggests future research directions. Key findings include the existence of critical mass thresholds, multistability, and the influence of network structure on contagion dynamics. The review underscores the importance of both theoretical and empirical approaches in advancing the understanding of higher-order contagion models.