Platforms have become a specific format of multi-sided markets in the 21st century digital economy. The paper provides theoretical examination of business and pricing models which underlie the success of many of modern fastestgrowing and most powerful companies such as Apple, Microsoft, Google, Amazon, eBay, Airbnb, Uber, Visa, Sony, etc. The author reviews four different types of multi-sided platforms: matching, multimedia, payment and software platforms. It is shown that platform business models are based on some unique features, including: technological infrastructure that provides interaction of agents; direct (among agents on the one side) and indirect (among agents on different sides) network externalities which make platforms more valuable to their customers; non-neutral price structure using to attract more clients on all sides. The author focuses on the main question determining the success of multi-sided platforms: how to create and monetize network externalities? It is stressed that the optimal platform price structure depends on the intensity of the indirect network externalities and the price sensitivity of agents. Special attention is paid to developing ways of launching a platform and monetizing the value created by network externalities. Basing on the platform economics statements, the author makes out two directions of the future “platform revolution”. The first direction will be the increasing competition among platforms that is no longer purely technological rivalry and a struggle for the critical mass of agents, which makes the platform viable. It is rapidly shifting towards service characteristics and prices. The second direction will be the dramatic growth of the business models associated with the Internet of things platforms (IoT-platforms).