Article 66 of the UCMJ mandates that each Judge Advocate General shall establish a Court of Criminal Appeals. The Courts of Criminal Appeals are staffed by senior judge advocates, normally in the grade of 0-5 and 0-6, and sit in three judge panels. These bodies are known as the Air Force Court of Criminal Appeals, the Army Court of Criminal Appeals, the Coast Guard Court of Criminal Appeals, and the Navy Court of Criminal Appeals (which also encompasses the Marines).
These service Courts of Criminal Appeals must review all cases where the judgement from a court-martial includes a sentence of death, dismissal of a commissioned officer, cadet, or midshipman, dishonorable discharge or bad-conduct discharge, or confinement for 2 years or more. A Court of Criminal Appeals will also have jurisdiction in timely appeals filed by convicted servicemembers who are sentenced to more than 6 months confinement but are not discharged, or in cases where the government had previously filed an appeal under Article 62.
Article 67 mandates review of service courts by the Court of Appeals for the Armed Forces (CAAF). This Court is composed of five civilians who are appointed by the president to 15-year terms, and confirmed by the Senate. They have jurisdiction over the service Court of Criminal Appeals, and also demonstrate the continued civilian control over the military, as these civilians, for all practical purposes, serve as the last check on military justice. (The U.S. Supreme Court has jurisdiction to oversee military cases, but rarely does so, and most appellants should not count on the Supreme Court hearing their case.)
All appellants have the right to petition CAAF within 60 days of the decision by the Court of Criminal Appeals. CAAF does not have to review all these cases, and practically only grants a small fraction of the petitions before it. However, CAAF must review all cases where an appellant was sentenced to death, and all cases certified for appeal by the Judge Advocate General of any one of the branches.
One of the distinctions between CAAF and the Courts of Criminal Appeals is the scope of their review. Article 66(d)(1) provides a positive mandate for the Courts of Criminal Appeals to affirm only such findings of guilt and the sentence as the Court finds correct in law and fact, and what it determines should be approved. This means these courts conduct a factual sufficiency review, to determine if there is sufficient evidence to prove guilt beyond a reasonable doubt. It also means they can determine the appropriateness of a sentence for reasons other than legal error. In contrast, Article 67(c)(4) provides CAAF may only take action with respect to matters of law. So CAAF does not have jurisdiction to conduct a factual sufficiency or sentence appropriateness review of the case.