  In this Chapter, we discuss the effects of higher-order structures on
SIS-like processes of social contagion. After a brief motivational introduction
where we illustrate the standard SIS process on networks and the difference
between simple and complex contagions, we introduce spreading processes on
higher-order structures starting from the most general formulation on
hypergraphs and then moving to several mean-field and heterogeneous mean-field
approaches. The results highlight the rich phenomenology brought by taking into
account higher-order contagion effects: both continuous and discontinuous
transitions are observed, and critical mass effects emerge. We conclude with a
short discussion on the theoretical results regarding the nature of the
epidemic transition and the general need for data to validate these models.
