The CJEU in Luxembourg consists of two major courts:

  1. the Court of Justice, informally known as European Court of Justice (ECJ), has the competence to hear applications from national courts for preliminary rulings on the interpretation of EU law, direct actions against EU member states for failure to fulfil an obligation, direct actions against EU institutions for annulment and for failure to act, as well as to hear appeals on points of law in rulings and orders of the General Court. The Court of Justice is composed of one judge from each EU member state (currently 27), assisted by 11 Advocates General. If assigned to a case, an Advocate General prepares an independent, non-binding opinion to assist the court in its deliberations.
  2. the General Court (EGC), known prior to the Treaty of Lisbon as the Court of First Instance, has the competence to hear actions brought by natural or legal persons against acts of EU institutions and agencies, actions brought by EU member states against the Commission or Council, actions for damages caused by EU institutions or agencies, actions relating to intellectual property, actions relating to employment and social security disputes between EU institutions and their staff, as well as limited applications from national courts for preliminary rulings. The General Court is composed of two judges from each EU member state (currently 54), though only 53 seats are currently filled. - Wikipedia 12/25

Tipp: For the international court of the Council of Europe (not a part of the EU universe) which interprets the European Convention on Human Rights, see European Court of Human Rights in Strasbourg