(CNN) President Donald Trump's nomination of Judge Neil Gorsuch to fill the Supreme Court has supporters and opponents alike digging into Gorsuch's record during his decade-long tenure on the Denver-based U.S. Court of Appeals for the 10th Circuit.

Some of his most notable opinions hit on the issues of religious liberty and the question how much deference courts should give to government agencies -- an area that could impact everything from environmental law and federal drug policy to highway safety and food inspection standards.

Here are five of Gorsuch's most notable cases:

Hobby Lobby Stores, Inc. v. Sebelius

One of the most striking and potentially controversial features of Gorsuch's jurisprudence is his overarching commitment to religious freedom as both a constitutional and statutory right -- even in contexts in which the Supreme Court had previously been less sympathetic to such claims.

In 2013, he joined in an opinion by the full Court of Appeals holding that federal law prohibited the Department of Health and Human Services from requiring closely-held, for-profit secular corporations to provide contraceptive coverage as part of their employer-sponsored health insurance plans.

And although a narrowly divided 5-4 Supreme Court would endorse that view (and affirm the 10th Circuit) the following year, Gorsuch wrote that he would have gone even further, and allowed not just the corporations, but the individual owners, to challenge the mandate.

As he opened his concurrence, "All of us face the problem of complicity. All of us must answer for ourselves whether and to what degree we are willing to be involved in the wrongdoing of others. For some, religion provides an essential source of guidance both about what constitutes wrongful conduct and the degree to which those who assist others in committing wrongful conduct themselves bear moral culpability."

Those religious beliefs, he concluded, justified allowing the individuals, and not just the corporations, to challenge the government's rules for employer-sponsored health insurance plans.

Yellowbear v. Lampert

Gorsuch's interest in religious freedom extends to the rights of prison inmates, as evidenced by his majority opinion in this case.

At issue was a Wyoming policy that prevented inmates housed in units other than the general population from accessing the sweat lodge in the prison yard -- a facility the plaintiff sought access to as part of his religious beliefs. Although the majority opinion conducted a straight-forward analysis to conclude that the policy violated the federal Religious Land Use and Institutionalized Persons Act (a holding the Supreme Court would shortly endorse in another case), Gorsuch went out of his way to explain the importance, to the plaintiff, of being able to practice his faith even (if not especially) from behind bars.

Thus, he opened the majority opinion by explaining that "Andrew Yellowbear will probably spend the rest of his life in prison. Time he must serve for murdering his daughter. With that much lying behind and still before him, Mr. Yellowbear has found sustenance in his faith. No one doubts the sincerity of his religious beliefs or that they are the reason he seeks access to his prison's sweat lodge -- a house of prayer and meditation the prison has supplied for those who share his Native American religious tradition. Yet the prison refuses to open the doors of that sweat lodge to Mr. Yellowbear alone, and so we have this litigation."

"While those convicted of crime in our society lawfully forfeit a great many civil liberties," Gorsuch added, "Congress has (repeatedly) instructed that the sincere exercise of religion should not be among them -- at least in the absence of a compelling reason. In this record we can find no reason like that."

Gutierrez-Brizuela v. Lynch

After his commitment to religious liberty, Gorsuch is perhaps best known for his strong views on one of the central questions of modern administrative law -- how much deference courts should give to government agencies when those agencies are acting within the authority delegated by Congress.

Even though the government has substantial power in the field of immigration, Gorsuch wrote the majority opinion in this technical case, which arose from disagreement between the courts and immigration authorities not over the substance of the rule at issue (a 10-year waiting period before those who had entered the country unlawfully more than once could be considered for some kind of lawful immigration status), but how that rule applied to cases pending when the rule was announced (but before it was confirmed by courts).

In a nutshell, Gorsuch held that immigration officials had exceeded their authority in applying their interpretation to cases pre-dating the courts' ruling, all the more so because the courts had already expressed skepticism about applying the new rule retroactively. In essence, the immigration authorities couldn't overrule the courts, even though it was on a question over which Congress had given the Executive Branch broad discretion. And although the immigration authorities' determination was loosely based upon a 2005 Supreme Court decision, Gorsuch wrote a separate concurrence to his own majority decision to criticize that decision -- and explain why it should be read narrowly.

As he explained, the Supreme Court's rulings deferring to agencies "permit executive bureaucracies to swallow huge amounts of core judicial and legislative power and concentrate federal power in a way that seems more than a little difficult to square with the Constitution of the framers' design. Maybe the time has come to face the behemoth."

His opposition to the Supreme Court's administrative law jurisprudence may have a more direct (and longer-lasting) impact if it finds additional support among current (and future) justices -- not just, as in this case, for immigration, but for regulations big and small.

United States v. Nichols

Another area in which Gorsuch has been openly critical of the Supreme Court's current jurisprudence is with respect to the "non-delegation doctrine" -- the idea that there should be limits on how much legislative power Congress should be allowed to delegate to the Executive Branch.

Since the 1930s, the Supreme Court has given Congress broad latitude on the theory that Congress is speaking as representatives of the people, and has generally allowed delegations of such power so long as there is some "intelligible principle" limiting the grant of authority. In this case, in a dissent from the full 10th Circuit's refusal to rehear a three-judge ruling with which he disagreed, Gorsuch strongly objected to how much regulatory power a federal statute -- the Sex Offender Registration and Notification Act (SORNA) -- gave to the Justice Department to apply its rules to those guilty of sex crimes predating the act's enactment.

In his words, "the framers of the Constitution thought the compartmentalization of legislative power not just a tool of good government or necessary to protect the authority of Congress from encroachment by the Executive but essential to the preservation of the people's liberty ...

"[B]y restricting lawmaking to one branch and forcing any legislation to endure bicameralism and presentment, the framers sought to make the task of lawmaking more arduous still. These structural impediments to lawmaking were no bugs in the system but the point of the design: a deliberate and jealous effort to preserve room for individual liberty."

As with his skepticism of judicial deference to agencies, Gorsuch's endorsement of a reinvigorated non-delegation doctrine would still put him at a distinct minority on the current Supreme Court -- but perhaps not for long.

One of the areas in which Justice Scalia's jurisprudence was, or at least appeared to be, the least partisan was with regard to the Fourth Amendment -- a context in which Scalia would often provide the more progressive justices with a fifth vote to invalidate a search or seizure that he deemed unconstitutional.

As a result, the Fourth Amendment is likely to be one of the contexts in which Gorsuch may well be the swing vote between two four-justice blocks. And if his dissenting opinion in this case is any guide, he may well continue Scalia's more libertarian tradition on searches and seizures. At issue was whether police officers were allowed to enter the area around the defendant's home (the "curtilage") before knocking on his door (usually, the answer is yes) if, as in that case, the defendant had prominently posted no-trespassing signs all over his property.

Although the majority held that the answer was yes, Gorsuch dissented. According to him, a property owner had the right to revoke the "implied license" of allowing potential visitors at least up to his front door, there was no precedent justifying the government's effort to "upend the original meaning of the Fourth Amendment or centuries of common law recognizing that homeowners may revoke by word or deed the licenses they themselves extend."

In that regard, he expanded upon the Supreme Court's own guidance in a 2013 opinion written for a 5-4 Court by... you guessed it... Antonin Scalia.

Steve Vladeck is a CNN contributor and professor of law at the University of Texas School of Law.