The article discusses some implications of the Brexit referendum for institutional and political development of the European Union and for relations between the EU and the UK. The most obvious consequence of the referendum is the collapse of ideology of continuous and progressing development of integration. Instead of endless, irreversible, a priori beneficial for everyone integration process, the European Union has become an organization that does not have a Messianic goal and obliged to prove its usefulness in everyday life. EU systemic crisis will inevitably lead to a profound transformation of its institutional and political structure. After the British referendum, only two options are possible. First of all, partial deconstruction of the European Union. The idea that European integration has gone too far lies in the basis of this strategy. According to this logic, the single market is the main EU achievement. Return to the basics - this is a pragmatic approach to integration, which should replace attempts to fix rotten projects (like Euro) or to achieve the unattainable (political Union). This option is hardly probable. Second option is transformation of the EU into the "core and periphery" system having the basis flexible integration. Over the past 20 years, flexibility transformed from temporary phenomenon into a permanent and formalized mechanism; its elements exist in many EU politics. Brexit would be able to accelerate significantly the formation of a cohesive core within the Eu. The core will not be homogeneous; it will include as governing structures: the German-French axis and a group of EU founding countries.