Why does Parliament move between Brussels and Strasbourg? 

The EU's national governments unanimously decided in 1992 to lay down in the EU treaty the official seats of the EU institutions.

When the European Coal and Steel Community (ECSC) was set up in the aftermath of WWII, in 1952, establishing joint management of the steel and coal reserves of six countries, its institutions were located in Luxembourg. The Council of Europe (an intergovernmental body made up of 46 countries championing human rights and culture) was also founded in the immediate post-WWII period. Based in Strasbourg, it offered its plenary chamber for meetings of the ECSC's "Common Assembly", which was to develop into the European Parliament. Strasbourg gradually became the main home of plenary sessions of the Parliament, though additional sessions were also held in Luxembourg in the 1960s and 1970s.

After the creation of the European Economic Community in 1958, much of the work done by the European Commission and the Council of Ministers came to be concentrated in Brussels. Since Parliament's work involves closely monitoring and interacting with both these institutions, over time Members decided to organise more of their work in Brussels. By the early 1990s, the present arrangement was more or less in place, with committees and political groups meeting in Brussels and the main plenary sessions taking place in Strasbourg. A major part of Parliament's staff is also based in Luxembourg.

The 1992 decision had important consequences for the working arrangements of the Parliament: its official seat and the venue for most of the plenary sessions became Strasbourg; parliamentary committees were to have their meetings in Brussels; and Parliament's Secretariat (its staff) would be officially based in Luxembourg. In 1997, this whole arrangement was incorporated into the EU treaty.

Any change to the current arrangements would mean changing the treaty, which requires unanimity among all Member State governments and ratification by each of their national parliaments.