[3][6] Boggs began his career with an academic position as a Bigelow Fellow and instructor at the University of Chicago Law School from 1968 to 1969.

[8] On January 29, 1986, Boggs was nominated by President Ronald Reagan to the United States Court of Appeals for the Sixth Circuit (Cincinnati, Ohio) to take a new seat authorized by 98 Stat.

[1][9] In 2006, Senator Mitch McConnell (R-KY) delivered on the Senate floor a tribute to Boggs to commemorate his 20-year anniversary on the federal bench, calling Judge Boggs "a Kentuckian who is one of the finest legal scholars of his generation," "a true Renaissance man" with a "fertile, polymath's mind," "[w]ell-read in history, geography, literature, mathematics, and political science," who "not only does … voraciously ingest knowledge, he loves to share it with others.

"[10] McConnell also noted that "Judge Boggs delights in hiring clerks of any and all political persuasions, as long as they have a keen mind and are always ready for debate.

"[10] On the occasion of Judge Boggs's 30th anniversary on the bench, Chief Justice Roberts wrote in a congratulatory letter: "The Nation has benefitted immeasurably from your intellect and judgment.

The divided Sixth Circuit, sitting en banc, reversed five to four in an opinion written by Chief Judge Boyce F. Martin Jr., which held that the Law School's admissions policy was narrowly tailored to serve its compelling interest in achieving a diverse student body, and that its policy was therefore valid.

Judge Boggs dissented, stating that the racial discrimination applied in the admissions policy of the law school would not pass even the slightest scrutiny, that the Law School's efforts to achieve a "critical mass" are functionally indistinguishable from an unconstitutional numerical quota for minorities, and that the majority opinion's analysis relying on the obscenity case Marks v. United States, 430 U.S. 188 (1977) was flawed.

Writing for the majority, Justice O'Connor held that the Law School had a compelling interest in attaining a diverse student body and that its admissions program was narrowly tailored to serve its compelling interest in obtaining the educational benefits that flow from a diverse student body, and thus did not violate the Equal Protection Clause.

Chief Justice Rehnquist, in his dissent, agreed with Judge Boggs's argument that the Law School's program bears little or no relation to its asserted goal of achieving "critical mass."

Analyzing admissions data, he noted that the Law School afforded preferential treatment to African American applicants but not to Hispanic or Native American candidates, failing to attempt to achieve any "critical mass" for these minority applicants, and failing to satisfy strict scrutiny analysis.

To solidify this point, Judge Boggs gave an example of a mixed-race applicant, whose ethnic origins would allow different racial categorizations by school administrators, resulting in discrimination for or against such candidate as permitted under existing precedent: one-half Chinese, one-fourth Eastern–European Jewish, one-eighth Hispanic (Cuban), and one-eighth general North European, mostly Scots–Irish.

Schuette v. Coalition to Defend Affirmative Action, Integration & Immigrant Rights & Fight for Equality By Any Means Necessary (BAMN), 572 U.S. 291 (2014).

The Supreme Court explained at length that the Sixth Circuit's extension of existing precedent was flawed and led to a mistaken conclusion.

Called upon to explore the jurisprudential twilight zone between two errant lines of precedent, we confront a frighteningly bizarre question: Does the Equal Protection Clause of the Fourteenth Amendment forbid what its text plainly requires?"

In this case concerning the constitutionality of a local ordinance brought by a billboard company, Judge Boggs followed a long history of his jurisprudence on First Amendment challenges to regulations of signage and advertising.

Writing for the majority, he held that the city ordinance regulating signs and billboards imposed a content-based restriction that is subject to strict scrutiny under the First Amendment.

Disagreeing with holdings by a few other circuits, Judge Boggs wrote that the Supreme Court precedent in Reed v. Town of Gilbert, Ariz., 135 S. Ct. 2218 (2015) rather than Central Hudson Gas & Electric Corp. v. Public Service Commission, 447 U.S. 557 (1980),  applied, as confirmed in the Supreme Court's more recent ruling in Barr v. American Association of Political Consultants, 140 S. Ct. 2335 (2020), requiring the application of strict rather than intermediate scrutiny to content-based restrictions on commercial speech.

The dissent did not address the standard of judicial review but instead concluded that the plaintiffs lacked standing to bring a challenge of the ordinance in the first place.

Boggs sparked controversy in 2001 by accusing then-Chief Judge Boyce F. Martin Jr. of violating Sixth Circuit procedural rules by assigning himself to panels, withholding from the full court information about en banc petitions, and manipulating the timing of orders.

[14] In both of these en banc cases Judge Boggs wrote a dissent that included a detailed description of the procedural irregularities involved.

[14][15] One unusual feature of Judge Boggs's managing style is a general knowledge quiz he gives to clerkship applicants.

"[16] Boggs's other clerks went on to become White House Counsel (Pat Cipollone), Director of National Intelligence in the Biden administration (Avril Haines), and Chairman of the Federal Energy Regulatory Commission (James Danly).