This survey deals with mathematical models for the formation of information communities under uncertainty. The models of opinion dynamics are considered in detail. Within these models, individuals change their opinions under the influence of other individuals in a social network of a nontrivial structure. Two classes of such models are presented: the models with rational (Bayesian) individuals and the models with naive (heuristic) individuals. For each of the classes, conditions for the formation of information communities in social networks are described. For various information communities to emerge in a society with rational agents, the rationality of individuals is often limited, and some assumptions on different awareness of individuals are introduced considering the network structure. For a society with naive individuals, different modifications of the opinion dynamics mechanism are often adopted.