When reviewing a sentence imposed by the district court, what is the role of the appellate court?

When reviewing a sentence imposed by the district court, "it is not the role of an appellate court to substitute its judgment for that of the sentencing court as to the appropriateness of a particular sentence; rather, in applying the Eighth Amendment the appellate court decides only whether the sentence under review is within constitutional limits." Solem v. Helm, 463 U.S. 277, 290 n. 16, 103 S.Ct. 3001, 3010 n. 16, 77 L.Ed.2d 637 (1983). For that reason, successful challenges to the constitutionality of particular sentences are extremely rare. See Hutto v. Davis, 454 U.S. 370, 374, 102 S.Ct. 703, 705, 70 L.Ed.2d 556 (1982).