Greater Europe refers to the idea of an extended or developed Europe

Europe

Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...

. This generally implies a Europe which transcends traditional boundaries, including trans-Eurasian countries, or those in close proximity with a strong European heritage.

It may specifically deal with future scenarios

Future enlargement of the European Union

The future enlargement of the European Union is theoretically open to any European country which is democratic, operates a free market and is willing and able to implement all previous European Union law...

 of enlargement

Enlargement of the European Union

The Enlargement of the European Union is the process of expanding the European Union through the accession of new member states. This process began with the Inner Six, who founded the European Coal and Steel Community in 1952...

 or development

European integration

European integration is the process of industrial, political, legal, economic integration of states wholly or partially in Europe...

 of the European Union

European Union

The European Union is an economic and political union of 27 independent member states which are located primarily in Europe. The EU traces its origins from the European Coal and Steel Community and the European Economic Community , formed by six countries in 1958...

, to the point of a Federal Europe or the Eurosphere

Eurosphere

The concept of the ‘Eurosphere’ or ‘European Empire’ has grown in popularity in the early years of the 21st century, and is associated with the public intellectual, Mark Leonard, the academic at the University of Oxford, Jan Zielonka, the strategist and European Union Director-General for...

, or a "re-unified" Europe

Europe

Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...

 after the fall of the Iron curtain

Iron Curtain

The concept of the Iron Curtain symbolized the ideological fighting and physical boundary dividing Europe into two separate areas from the end of World War II in 1945 until the end of the Cold War in 1989...

.