The Federal Constitutional Court
The Federal Constitutional Court (Bundesverfassungsgericht, or BVerfG) is Germany's Supreme Court, and its role is essentially "Guardian of the Constitution".
A case coming before the Court may be heard by one of its two Senates, or for important cases, by the Court in plenary session. There are 16 judges divided equally between the two senates, and they each hold office for a non-renewable period of 12 years. Half the judges are elected by the Bundestag (the directly elected lower house of the parliament), and half are elected by the Bundesrat (the upper house made up of representatives from the state governments). In both cases, the judges are elected by a two-thirds majority, a procedure which leads to much hard-bargaining between the major political parties as to the choice of judges, since no single party can command such a majority.
The Court's principal areas of jurisdiction are laid down in Article 93 I of the Constitution (Grundgesetz). These areas are also detailed, along with all the Court's procedures, in the Statute of the Court (Bundesverfassungsgerichtgesetz, or BVerfGG). The six main juridictions are:
1. Disputes between federal organs of the State as to their duties and reponsibilities under the Constitution.(Organstreitigkeiten)
2. Disputes between the federal states (Länder) and the federation (Bund), as to their relationship and the division of responsibilities between them under the Constitution (bundesstaatliche Streitigkeiten).
3. Verifying the compatibility of (federal or state) laws and regulations with the Constitution. This is exceptionally available on an abstract basis to a limited group of bodies, but is more normally available on a concrete basis for cases referred by a lower court, where the lower court believes a law to be in breach of the constitution, and this question is central to the case. (abstrakte und konkrete Normenkontrolle)
4. A complaint of unconstitutionality can be brought by any person believing his or her fundamental rights to have been infringed by the act of a public authority, and who has exhausted other routes to a legal remedy. For the purposes of this jurisdiction, Article 93 I not only refers to the fundamental rights listed in Arts 1-19 of the Constitution, but also Arts. 20, 33, 38, 101, 103, and 104. (Verfassungsbeschwerde)
5. An indictment procedure is also exceptionally available against the Federal President or judges acting in breach of the Constitution. Controversially, this jurisdiction has also twice been used to ban political parties (Sozialistische Reichspartei and Kommunistische Partei Deutschlands) threatening the Constitution. (Anklageverfahren)
6. Other miscellaneous procedures, including verifying the decisions of the Bundestag. (Wahlprüfungsverfahren)
For more information (in English) on the Federal Constitutional Court, a good starting point is "Facts about Germany"
The German Federal Constitution - full English text of the Grundgesetz
Federal Constitutional Court Reports - the BVerfG's full press releases on its decisions (in German)
Reports of the Federal Constitutional Court - - English abstracts of the official press releases from the BVerfG (translated by Alex Caviedes), see also http://www.jura.uni-sb.de/lawweb/pressreleases/
Federal Constitutional Court Case Law - detailed discussion in German of a wide range of BVerfG cases, each with a brief English abstract (from Uni.Wuerzburg)