Abstention doctrine

An abstention doctrine is any of several doctrines that a United States court may (or in some cases must) apply to refuse to hear a case if hearing the case would potentially intrude upon the powers of another court. Such doctrines are usually invoked where lawsuits involving the same issues are brought in two different court systems at the same time (such as federal and state courts).
The United States has a federal court system with limitations on the cases that it can hear, while each state has its own individual court system. In some instances, the jurisdiction of these courts overlap, so a lawsuit between two parties may be brought in either or both courts. The latter circumstance can lead to confusion, waste resources, as well as cause the appearance that one court is disrespecting the other. Both federal and state courts have developed rules determining when one court will defer to another's jurisdiction over a particular case.
Federal abstention doctrines.
The various abstention doctrines applied by federal courts are named for the United States Supreme Court cases in which they were enunciated.
"Pullman" abstention.
"Pullman" abstention was the first "doctrine of abstention" to be announced by the Court, and is named for "Railroad Commission v. Pullman Co.", 312 U.S. 496 (1941). Concisely, the doctrine holds that "the federal courts should not adjudicate the constitutionality of state enactments fairly open to interpretation until the state courts have been afforded a reasonable opportunity to pass on them." This doctrine permits a federal court to stay a plaintiff's claim that a state law violates the United States Constitution until the state's judiciary has had an opportunity to apply the law to the plaintiff's particular case. The hope is to avoid a federal constitutional ruling by allowing the state courts to construe the law in a way that eliminates the constitutional problem or to rule it void under the state's own constitution.
For "Pullman" abstention to be invoked, three conditions must be apparent:
Under "Pullman" abstention, the federal court retains jurisdiction to hear the constitutional issues in the case if the state court's resolution is still constitutionally suspect. In "Government and Civil Employees Organizing Committee, CIO v. Windsor", 353 U.S. 364 (1957), the Supreme Court held that litigants must "inform" the state court that they are contending that the state law violates a federal constitutional provision, so that the state court may take that into consideration when interpreting the state statute. However, in "England v. Louisiana State Board of Medical Examiners", 375 U.S. 411 (1964), the Supreme Court noted that the litigants must not ask the state court to "resolve" the constitutional issue itself, or the federal court would be bound by "res judicata" to follow the decision of the state court. In such a case, the litigant seeking a judgment that the law is unconstitutional must usually appeal to the higher courts of the state, rather than seeking review in a federal court.
"Younger" abstention.
"Younger" abstention, named for "Younger v. Harris", 401 U.S. 37 (1971), is less permissive to the federal courts, barring them from hearing civil rights tort claims brought by a person who is currently being prosecuted for a matter arising from that claim in state court. For example, if an individual who was charged with drug possession under a state law believes that the search was illegal, and in violation of their Fourth Amendment rights, that person may have a cause of action to sue the state for illegally searching him. However, a federal court will not hear the case until the person is convicted of the crime. The doctrine has been extended to state civil proceedings in aid of and closely related to state criminal statutes, administrative proceedings initiated by a state agency, or situations where the State has jailed a person for contempt of court. The doctrine applies even where the state does not bring an action until after the person has filed a lawsuit in federal court, provided that the federal court has not yet undergone proceedings of substance on the merits of the federal suit.
There are three exceptions to "Younger" abstention:
"Younger" abstention later extended to a defendant in state court's civil action (not just a criminal case) in three "exceptional circumstances", see "Sprint Communications, Inc. v. Jacobs" (2013) 571 U.S. 69, 78, because that defendant can and should raise constitutional rights as defense in the same state court proceeding.
"Burford" abstention and "Thibodaux" abstention.
"Burford" abstention, derived from "Burford v. Sun Oil Co.", 319 U.S. 315 (1943), allows a federal court to abstain in complex administrative processes (the case itself dealt with the regulation of oil drilling operations in Texas). "Burford" allows a federal court to dismiss a case only if:
"Burford" abstention is closely related to "Thibodaux" abstention, derived from "Louisiana Power & Light Co. v. City of Thibodaux", 360 U.S. 25 (1959), which occurs when a federal court sitting in diversity jurisdiction chooses to allow a state to decide issues of state law that are of great public importance to that state, to the extent that a federal determination would infringe on state sovereignty. 
Unlike the abstention doctrines raised in federal question cases, there is a strong presumption that federal courts should "not" apply "Burford" or "Thibodaux" Abstention.
"Colorado River" abstention.
Finally, "Colorado River" abstention, from "Colorado River Water Conservation District v. United States", 424 U.S. 800 (1976) comes into play where parallel litigation is being carried out, particularly where federal and state court proceedings are simultaneously being carried out to determine the rights of parties with respect to the same questions of law. Under such circumstances, it makes little sense for two courts to expend the time and effort to achieve a resolution of the question.
Unlike other abstention doctrines, application of the "Colorado River" doctrine is prudential and discretionary, and is based less on comity or respect between different court systems than on the desire to avoid wasteful duplication of litigation. The classification of the doctrine as a form of abstention has been disputed, with some courts simply calling it a "doctrine of exceptional circumstances". Each of the various federal circuits has come up with its own list of factors to weigh in determining whether a federal court should abstain from hearing a case under this doctrine. Typically, such factors include:
Ecclesiastical abstention.
Under the ecclesiastical abstention doctrine, civil courts cannot delve into matters that focus on "theological controversy, church discipline, ecclesiastical government, or the conformity of the members of a church to the standard of morals required of them." More specifically, the courts generally agree that they cannot (a) consider employment disputes between a religious institution and its clergy, (b) resolve conflicts between different factions within a religious organization, (c) resolve property disputes that would require the court to interpret religious doctrine, or (d) resolve contract disputes that involve membership in a religious institution. Inserting the court’s secular values into religious affairs, the rationale goes, would inject the "power of the state into the forbidden area of religious freedom contrary to the principles of the First Amendment."
The courts, however, have split on two important issues concerning the ecclesiastical abstention doctrine: (1) whether the doctrine provides religious officials with immunity from defamation suits when the allegedly defamatory statement was made during a religious proceeding; and (2) whether the doctrine prevents religious institutions from being sued for negligently hiring, retaining, or supervising members of their clergy. This latter issue is particularly important given the "tidal wave of litigation" that followed the Catholic Church's sexual abuse scandals. At least one scholar has argued that the ecclesiastical abstention doctrine should not shield religious organizations from lawsuits for negligently hiring, retaining, or supervising their clergy, especially in cases involving child molestation. 
For an overview of the ecclesiastical abstention doctrine, see Alexander J. Lindvall, "Forgive Me, Your Honor, For I Have Sinned: Limiting the Ecclesiastical Abstention Doctrine to Allow Suits for Defamation and Negligent Employment Practices", 72 South Carolina Law Review 25, 29–35 (2020).
Note on the "Rooker-Feldman" doctrine.
The "Rooker-Feldman" doctrine has some characteristics of an abstention doctrine, because it prohibits federal court review of state court actions. However, it does not require federal courts to abstain from hearing cases pending action in the state court, but instead deems that federal courts lack jurisdiction to hear cases already fully decided in state courts. The doctrine is not a judicially created exception to federal jurisdiction. Rather, the Rooker and Feldman cases simply recognized the fact that Congress has not granted the federal district or appeals courts statutory jurisdiction to consider appeals of state court decisions, only the US Supreme Court via a writ of "certiorari"). It is an open question whether Congress could grant such jurisdiction.
State court abstention doctrines.
No national rule requires state courts to abstain from hearing cases brought in federal courts or in courts of other states, though the All Writs Act permits federal courts to enjoin state courts from hearing matters if necessary to preserve the jurisdiction of the federal court. But every state has some doctrine that lets its courts stay actions to avoid duplicative litigation.
Some states have doctrines that let state courts abstain from hearing cases already pending in other kinds of tribunals. For example, in "Gavle v. Little Six, Inc.," 555 N.W.2d 284 (Minn. 1996), the Minnesota Supreme Court upheld abstention where the state court might "undermine the authority of the tribal courts over Reservation affairs" or "infringe on the right of Indians to govern themselves".