In this talk, we first discuss a classical model of opinion dynamics in social networks and we establish new necessary and sufficient conditions for its stability and convergence. Subsequently, we propose a novel multidimensional model based on a correlation matrix, which takes into account (two or more) interdependent topics describing human attitudes and beliefs on multiple issues. We establish the system-theoretic properties of this multidimensional model and we show that the correlation matrix can be computed by means of a convex optimization program. Although the multidimensional model requires the agents to communicate synchronously, we demonstrate that the same final opinions can be obtained using a decentralized asynchronous gossip-based protocol.