Rapid development of the platform economy leads to changes in the organizational forms of the economy that are followed by a fundamental transformation of social relationships on macro and micro levels, directly affecting a major subject area of sociology. Extraction of big data by the platforms gives an access to examination of human behavior, which was hardly accessible in previous times. At the same time, it claims for new analytical approaches. As a result, sociology is facing serious substantive and methodological challenges. More effective analysis of dynamic changes in the environment is required. Maintenance of the sociological theory itself as a corpus of general explanatory schemes is also on the agenda given the increasing attempts to replace sociology by the computational social science. Presented study is based on a most recent special literature. We define platforms as a new mode of economic integration, trace a logic of the platform capitalism, examine the emerging hybrid forms of exchange, reveal a contradictory nature of the social networks, explore the new meanings of rationality of human behavior, and analyze how social relationships are being changed at different levels.