Appellant Danny Clifton filed an application for Social Security benefits, alleging a disability beginning on June 30, 1991, due to a back injury. After a hearing, an administrative law judge (ALJ) concluded at step five of the five-part sequential evaluation process, see 20 C.F.R. 404.1520; Williams v. Bowen, 844 F.2d 748, 750-52 (10th Cir.1988), that appellant could still perform limited sedentary work and, therefore, was not disabled. Because the Appeals Council denied review, the ALJ’s decision became the Secretary’s final decision. Appellant appeals from the district court’s order affirming the Secretary’s decision to deny him disability bene[*1009] fits. We have jurisdiction under 42 U.S.C. 405(g) and 28 U.S.C. 1291. We reverse. ^[1]

Appellant argues on appeal that the district court erred in affirming the Secretary’s determinations that: (1) appellant’s impairments did not meet or equal Listed Impairment 1.05(C) (vertebrogenie disorders), 20 C.F.R. Pt. 404, Subpt. P, App. 1; and (2) appellant retained the residual functional capacity (RFC) to perform a limited range of sedentary, unskilled work that exists in significant numbers in the national economy.

At step three, the ALJ determines whether the claimant’s impairment “is equivalent to one of a number of listed impairments that the Secretary acknowledges as so severe as to preclude substantial gainful activity.” Williams, 844 F.2d at 751 (quotation omitted). In this case, the ALJ did not discuss the evidence or his reasons for determining that appellant was not disabled at step three, or even identify the relevant Listing or Listings; he merely stated a summary conclusion that appellant’s impairments did not meet or equal any Listed Impairment. Appellant’s App. at 18-19. Such a bare conclusion is beyond meaningful judicial review. Under the Social Security Act,

[t]he Commissioner of Social Security is directed to make findings of fact, and decisions as to the rights of any individual applying for a payment under this sub-chapter. Any such decision by the Commissioner of Social Security which involves a determination of disability and which is in whole or in part unfavorable to such individual shall contain a statement of the ease, in understandable language, setting forth a discussion of the evidence, and stating the Commissioner’s determination and the reason or reasons upon which it is based.

42 U.S.C. 405(b)(1). Under this statute, the ALJ was required to discuss the evidence and explain why he found that appellant was not disabled at step three. Cook v. Heckler, 783 F.2d 1168, 1172-73 (4th Cir.1986); see also Brown v. Bowen, 794 F.2d 703, 708 (D.C.Cir.1986) (relying upon 20 C.F.R. 404.953 and 5 U.S.C. 557(c)[ (3)(A) ] to hold that an ALJ must explain his adverse decisions).

This statutory requirement fits hand in glove with our standard of review. By congressional design, as well as by administrative due process standards, this court should not properly engage in the task of weighing evidence in cases before the Social Security Administration. 42 U.S.C. 405(g) (“The findings of the Commissioner of Social Security as to any fact, if supported by substantial evidence, shall be conclusive.”); Cagle v. Califano, 638 F.2d 219, 220 (10th Cir.1981) (holding court does not weigh the evidence or substitute its judgment for that of the Secretary); see also Consolo v. Federal Maritime Comm’n, 383 U.S. 607, 619-20, 86 S.Ct. 1018, 1026, 16 L.Ed.2d 131 (1966) (discussing similar “substantial evidence” standard under the Administrative Procedure Act, now codified at 5 U.S.C. 706(2)(E)). Rather, we review the Secretary’s decision only to determine whether her factual findings are supported by substantial evidence and whether she applied the correct legal standards. 42 U.S.C. 405(g); see also Byron v. Heckler, 742 F.2d 1232, 1234-35 (10th Cir.1984).

Substantial evidence “‘means such relevant evidence as a reasonable mind might accept as adequate to support a conclusion.’ ” Richardson v. Perales, 402 U.S. 389, 401, 91 S.Ct. 1420, 1427, 28 L.Ed.2d 842 (1971) (quoting Consolidated Edison Co. v. NLRB, 305 U.S. 197, 229, 59 S.Ct. 206, 217, 83 L.Ed. 126 (1938)). In the absence of ALJ findings supported by specific weighing of the evidence, we cannot assess whether relevant evidence adequately supports the ALJ’s conclusion that appellant’s impairments did not meet or equal any Listed Impairment, and whether he applied the correct legal standards to arrive at that conclusion. The record must demonstrate that the ALJ considered all of the evidence, but an ALJ is not required to[*1010] discuss every piece of evidence. Vincent ex rel. Vincent v. Heckler, 739 F.2d 1393, 1394-95 (9th Cir.1984). Rather, in addition to discussing the evidence supporting his decision, the ALJ also must discuss the uncontro-verted evidence he chooses not to rely upon, as well as significantly probative evidence he rejects. Id.; see also Zblewski v. Schweiker, 732 F.2d 75, 79 (7th Cir.1984) (“a minimal level of articulation of the ALJ’s assessment of the evidence is required in cases in which considerable evidence is presented to counter the agency’s position”). Therefore, the case must be remanded for the ALJ to set out his specific findings and his reasons for accepting or rejecting evidence at step three.

Because we reverse and remand for additional proceedings at step three, it is unnecessary for us to reach appellant’s contentions of error at step five. We note without deciding, however, that appellant appears to have raised a meritorious argument that some of the medical evidence the ALJ relied on was taken out of context, and other medical evidence was rejected without explanation.

The judgment of the United States District Court for the District of Kansas is REVERSED, and the case is REMANDED to the district court with directions to remand to the Secretary for additional proceedings consistent with this opinion.