The European Council
The first Councils were held in February and July 1961 (in Paris and Bonn respectively). They were informal summits of the leaders of the European Community and were started due to then-French President Charles de Gaulle's resentment at the domination of supranational institutions (e.g. the European Commission) over the integration process. The first influential summit was held in 1969 after a series of irregular summits. The Hague summit of 1969 reached an agreement on the admittance of the United Kingdom into the Community and initiated foreign policy co-operation (the European Political Cooperation) taking integration beyond economics.
The summits were only formalised in 1974, at the December summit in Paris, following a proposal from then-French President Valéry Giscard d'Estaing. It was felt that more inter-governmental input was needed following the "empty chair crisis" and economic problems. The inaugural Council, as it had become, was held in Dublin on 1975-03-10/1975-03-11 during Ireland's first Presidency of the Council of the European Union. In 1987 it was included in the treaties for the first time (the Single European Act) and had a defined role for the first time in the Maastricht Treaty. At first only two meetings per year were required, now there are on average four European Councils each year (two per presidency). The seat of the Council was formalised in 2002, basing it in Brussels (see Seat). In addition to usual councils, there are the occasional extraordinary councils, for example in 2001 the European Council gathered to lead the EU's response to those events.
The European Council isn't an official institution of the EU, although it is mentioned in the treaties as a body which "shall provide the Union with the necessary impetus for its development". Essentially it defines the EU's policy agenda and has thus been considered to be the motor of European integration. It does this without any formal powers, only the influence it has by being composed of national leaders. Beyond the need to provide "impetus", the Council has developed further roles; to "settle issues outstanding from discussions at a lower level", to lead in foreign policy - acting externally as a "collective Head of State", "formal ratification of important documents" and "involvement in the negotiation of the treaty changes".
Since the body is composed of national leaders, it brings together the executive power of the member states, having a great deal of influence outside the European Community: for example over foreign policy and police & justice. It also exercises the more executive powers of the Council of the European Union (the European Council could be described as a configuration of that body) such as the appointment of the President of the European Commission. Hence with powers over the supranational executive of the EU, in addition to its other powers, the European Council has been described by some as the Union's "supreme political authority".
However, the body has been criticised by some for a lack of leadership, in part stemming from the weak structure of the body, meeting only 4 times a year for 2 days with no staff and no legislative decisions made.