Abstract: Random graphs are useful models for complex networks appearing in empirical studies of networks. Several structural properties have been identified in this context, including scale-free and small-world properties. In this talk I will describe the Ising model on random graphs satisfying these properties. The Ising model is a stochastic model introduced in statistical physics to model phase transitions. Thus two sources of randomness are intertwined in the Ising model on random graphs. I will investigate their interplay studying the Boltzmann-Gibbs measure for a fixed random graph realization or when the average over graphs (quenched or annealed) is performed. I shall focus on universality, proving law of large numbers and central limit theorems in the uniqueness phase, as well as non-classical limit theorems at criticality.