This work represents a survey of the social network analysis problem. There are four main approaches: structural, resource-based, regulatory, and dynamic. To solve the problems in social network analysis, the following methods are used: graph and stochastic models, models of network evolution, methods involving ontologies, structural and relational models, machine learning methods, network visualization techniques, etc. The paper also describes the most popular computer social networks and some software applications to analyze them. It presents some possible paths of research: creation of an integrated theory of social networks, adaptation of methods of natural language text processing to the online content, etc.