The Federal Supreme Court is a Constitutional Court originally established under Article 44 of the Transitional Administrative Law (TAL) and Law No. 30 of 2005, an order of the Transitional Government made under the TAL. The TAL, which had been signed on 8 March 2004 by the Iraqi Governing Council, came into effect on 28 June 2004 and remained in place until the 2005 Constitution came into effect. The Court is now firmly established under Articles 92 to 94 of the 2005 Constitution.
Article 92 (Second) of the 2005 Constitution states that:

The Federal Supreme Court shall be made up of a number of judges, experts in Islamic jurisprudence, and legal scholars, whose number, the method of their selection, and the work of the Court shall be determined by a law enacted by a two-thirds majority of the members of the Council of Representatives.

However no such law has yet been enacted and the experts in Islamic Jurisprudence and Legal Scholars have not yet been incorporated into the operation of the court.

At present, there are 9 members of the Federal Supreme Court. The court issued rules of procedure in 2005 which were published in the Official Gazette issue 3997 of 2 May 2005.
Article 93 of the Constitution sets out the jurisdiction of the Federal Supreme Court as follows:

First: Overseeing the constitutionality of laws and regulations in effect.
Second: Interpreting the provisions of the Constitution.
Third: Settling matters that arise from the application of the federal laws, decisions, regulations, instructions, and procedures issued by the federal authority. The law shall guarantee the right of direct appeal to the Court to the Council of Ministers, those concerned individuals, and others.
Fourth: Settling disputes that arise between the federal government and the governments of the regions and governorates, municipalities, and local administrations.
Fifth: Settling disputes that arise between the governments of the regions and governments of the governorates.
Sixth: Settling accusations directed against the President, the Prime Minister and the Ministers, and this shall be regulated by law.
Seventh: Ratifying the final results of the general elections for membership in the Council of Representatives.
Eight:
A. Settling competency disputes between the federal judiciary and the judicial institutions of the regions and governorates that are not organized in a region.
B. Settling competency disputes between judicial institutions of the regions or governorates that are not organized in a region.

Further analysis of the federal judiciary in general and the Federal Supreme Court in particular can be found on the judicial independence page of this site.
The Federal Supreme Court website records: Decisions and Judgments; Opinions relating to constitutional interpretation; and Appeal Judgements from the Administrative Court Function of the Shura Council.

• Index of Decisions
  • 2005
  • 2006
  • 2007
  • 2008
  • 2009
• Decisions
  • 1/2005: Regarding Article 136(b) of the Criminal Procedure Code العربية
  • 15/2006: decision regarding size and composition of the CoR العربية
  • 58/2009: regarding the governor of Salah Al-Din العربية

• Opinions
  • 29/2009: On the date of the 2010 national election (العربية)
  • 72/2009: On the manner of seat allocation proposed in the draft election amendment law (العربية)
  • 76/2009: On the correct interpretation of the 10 day time period for Presidency Council veto (العربية)
  • 25/2010: On the selection of the nominee of the largest bloc after the election (العربية)

Note that the Federal Supreme Court is the second Constitutional Court to have been established in Iraq. Law No. 159 of 1968 established a Supreme Constitutional Court not long after the Ba’athist takeover of the government. It operated for a short period but we do not have any of its decisions.