APA judicial review is not available when statutes preclude judicial review and when agency action is committed to the agency discretion by law.
A statute may explicitly preclude review but that does not stop any other types of challenges such as constitutionality of the statute itself. See Johnson v. Robinson, 415 U.S. 361 (1974).
'[A]djudication of the constitutionality of congressional enactments has generally been thought beyond the jurisdiction of administrative agencies. See Public Utilities Comm'n v. United States, 355 U. S. 534, 355 U. S. 539 (1958); Engineers Public Service Co. v. SEC, 78 U.S.App.D.C.199, 215-216, 138 F.2d 936, 952-953 (1943), dismissed as moot, 332 U.S. 788.' Oestereich v. Selective Service Board, 393 U. S. 233, 393 U. S. 242 (1968) (Harlan, J., concurring in result); see Jaffe, Judicial Review: Question of Law, 69 Harv.L.Rev. 239, 271-275 (1955).
The Administrative Procedure Act provides that the provisions of the Act authorizing judicial review apply 'except to the extent that -- (1) statutes preclude judicial review; or (2) agency action is committed to agency discretion by law.' 5 U.S.C. § 701(a) (1964 ed., Supp. IV). In Shaughnessy v. Pedreiro, 349 U. ...