Historically, the development of the circular economy (CE) proceeds from the CE 1.0 stage, characterized by attention to waste management and recycling, to the CE 2.0 stage with an emphasis on resource efficiency and eco-efficiency, to the current CE 3.0 stage, in which the key factor to a company’s success is the business model. However, not all countries of the world simultaneously began transforming the national economy from a linear model to a circular one; many are still at the CE 1.0 and CE 2.0 stages, and do not have a developed system of institutions supporting the circular economy. In Russia, the concept of a circular economy has not yet received recognition in society and government; the stage of its development can be defined as CE 2.0. This study compares the barriers and drivers of CE development in the EU countries, a group of countries with a well-developed institutional support system, and in Russia, a country that does not have such a system. The study reveals that the most significant difference between countries with mature systems of institutional support and Russia lies in the regulatory sphere and in information and awareness about new available technologies and ways to increase resource efficiency, commercial attractiveness, and organizational feasibility. Changes in the first sphere are impossible without the participation of the national authorities; however, changes in the information sphere are feasible even without the government’s support. The actors in such changes can be international companies with access to resource-efficient new technologies and processes for organizing business.