Geneva Conventions
The protecting power is a mediator enabling the flow of communication between the parties to the conflict. The protecting power also monitors the implementation of these Conventions, such as by visiting the zone of conflict and prisoners of war. The protecting power must act as an advocate for prisoners, the wounded, and civilians.

Grave breaches: Not all violations of the treaty are treated equally. The most serious crimes are termed grave breaches and provide a legal definition of a war crime. Grave breaches of the Third and Fourth Geneva Conventions include the following acts if committed against a person specifically protected by the conventions: 

willful killing, torture or inhumane treatment, including biological experiments
willfully causing great suffering or serious injury to body or health
compelling a protected person to serve in the armed forces of a hostile power
willfully depriving a protected person of the right to a fair trial if accused of a war crime.
Also considered grave breaches of the Fourth Geneva Convention are the following:

taking of hostages
extensive destruction and appropriation of property not justified by military necessity and carried out unlawfully and wantonly
unlawful deportation, transfer, or confinement.
Nations that are party to these treaties must enact and enforce legislation penalizing any of these crimes. Nations are also obligated to search for persons alleged to commit these crimes, or persons having ordered them to be committed, and to bring them to trial regardless of their nationality and regardless of the place where the crimes took place.
The principle of universal jurisdiction also applies to the enforcement of grave breaches when the United Nations Security Council asserts its authority and jurisdiction from the UN Charter to apply universal jurisdiction. The UNSC did this when they established the International Criminal Tribunal for Rwanda and the International Criminal Tribunal for the former Yugoslavia to investigate and/or prosecute alleged violations.

Right to a fair trial when no crime is alleged: Soldiers, as prisoners of war, will not receive a trial unless the allegation of a war crime has been made. According to article 43 of the 1949 Conventions, soldiers are employed for the purpose of serving in war; engaging in armed conflict is legitimate, and does not constitute a grave breach. Should a soldier be arrested by belligerent forces, they are to be considered "lawful combatants" and afforded the protectorate status of a prisoner of war (POW) until the cessation of the conflict. Human rights law applies to any incarcerated individual, including the right to a fair trial. 
Charges may only be brought against an enemy POW after a fair trial, but the initial crime being accused must be an explicit violation of the accords, more severe than simply fighting against the captor in battle. No trial will otherwise be afforded to a captured soldier, as deemed by human rights law. This element of the convention has been confused during past incidents of detainment of US soldiers by North Vietnam, where the regime attempted to try all imprisoned soldiers in court for committing grave breaches, on the incorrect assumption that their sole existence as enemies of the state violated international law.

Legacy: Although warfare has changed dramatically since the Geneva Conventions of 1949, they are still considered the cornerstone of contemporary international humanitarian law. They protect combatants who find themselves hors de combat, and they protect civilians caught up in the zone of war. These treaties came into play for all recent non-international armed conflicts, including the War in Afghanistan, the Iraq War, the invasion of Chechnya (1994–2017), and the Russo-Georgian War. The Geneva Conventions also protect those affected by non-international armed conflicts such as the Syrian civil war.
The lines between combatants and civilians have blurred when the actors are not exclusively High Contracting Parties (HCP). Since the fall of the Soviet Union, an HCP often is faced with a non-state actor, as argued by General Wesley Clark in 2007. Examples of such conflict include the Sri Lankan Civil War, the Sudanese Civil War, and the Colombian Armed Conflict, as well as most military engagements of the US since 2000.
Some scholars hold that Common Article 3 deals with these situations, supplemented by Protocol II (1977). These set out minimum legal standards that must be followed for internal conflicts. International tribunals, particularly the International Criminal Tribunal for the former Yugoslavia (ICTY), have clarified international law in this area. In the 1999 Prosecutor v. Dusko Tadic judgement, the ICTY ruled that grave breaches apply not only to international conflicts, but also to internal armed conflict. Further, those provisions are considered customary international law.
Controversy has arisen over the US designation of irregular opponents as "unlawful enemy combatants" (see also unlawful combatant), especially in the SCOTUS judgments over the Guantanamo Bay detention camp brig facility Hamdi v. Rumsfeld, Hamdan v. Rumsfeld and Rasul v. Bush, and later Boumediene v. Bush. President George W. Bush, aided by Attorneys-General John Ashcroft and Alberto Gonzales and General Keith B. Alexander, claimed the power, as Commander in Chief of the Armed Forces, to determine that any person, including an American citizen, who is suspected of being a member, agent, or associate of Al Qaeda, the Taliban, or possibly any other terrorist organization, is an "enemy combatant" who can be detained in U.S. military custody until hostilities end, pursuant to the international law of war.
The application of the Geneva Conventions in the Russo-Ukrainian War (2014–present) has been troublesome because some of the personnel who engaged in combat against the Ukrainians were not identified by insignia, although they did wear military-style fatigues. The types of comportment qualified as acts of perfidy under jus in bello doctrine are listed in Articles 37 through 39 of the Geneva Convention; the prohibition of fake insignia is listed at Article 39.2, but the law is silent on the complete absence of insignia. The status of POWs captured in this circumstance remains a question.
Educational institutions and organizations including Harvard University, the International Committee of the Red Cross, and the Rohr Jewish Learning Institute use the Geneva Convention as a primary text investigating torture and warfare.

New challenges: Artificial intelligence and autonomous weapon systems, such as military robots and cyber-weapons, are creating challenges in the creation, interpretation and application of the laws of armed conflict. The complexity of these new challenges, as well as the speed in which they are developed, complicates the application of the Conventions, which have not been updated in a long time. Adding to this challenge is the very slow speed of the procedure of developing new treaties to deal with new forms of warfare, and determining agreed-upon interpretations to existing ones, meaning that by the time a decision can be made, armed conflict may have already evolved in a way that makes the changes obsolete.

See also: Attacks on humanitarian workers
Convention on Certain Conventional Weapons
Customary international humanitarian law
Declaration on the Protection of Women and Children in Emergency and Armed Conflict
Geneva Conference (disambiguation)
Geneva Academy of International Humanitarian Law and Human Rights
German Prisoners of War in the United States
Hague Conventions of 1899 and 1907 – traditional rules on fighting wars
Human rights
Human shield
International Committee of the Red Cross
International Federation of Red Cross and Red Crescent Societies
International humanitarian law
Laws of war
Lieber Code General Order 100
Nuremberg Principles
Reprisals
Rule of Law in Armed Conflicts Project
Saint Petersburg Declaration of 1868
Targeted killing

References: 

Further reading: Matthew Evangelista and Nina Tannenwald (eds.). 2017. Do the Geneva Conventions Matter? Oxford University Press.
Giovanni Mantilla, "Conforming Instrumentalists: Why the USA and the United Kingdom Joined the 1949 Geneva Conventions," European Journal of International Law, Volume 28, Issue 2, May 2017, Pages 483–511.
Helen Kinsella, "The image before the weapon : a critical history of the distinction between combatant and civilian" Cornell University Press.
Boyd van Dijk (2022). Preparing for War: The Making of the Geneva Conventions. Oxford University Press.

External links: 
 The Geneva Conventions of 12 August 1949 public domain audiobook at LibriVox
Texts and commentaries of 1949 Conventions & Additional Protocols
The Geneva Conventions: the core of international humanitarian law, ICRC
Rules of war (in a nutshell)—video
Commentaries:
GCI: Commentary
GCII: Commentary
GCIII: Commentary
GCIV: Commentary