War crimes, as we understand it now, are grave transgressions against international public law in the context of armed conflicts. Overtime (details will follow) they have "split up" into war crimes, crimes against peace (basically starting a war), crimes against humanity (acts against civilian populations in times of peace or war) and genocide.

They are a construct of international public law - the law that regulates the legal relations of nation states. There is no elected legislator; the states themselves created these laws over time mostly by signing treaties and adhering to international customs (while being convinced, they have to). Nowadays war crimes are forbidden everywhere, every state is bound by those rules ("ius cogens"), however there is no competent court. (There is the International Criminal Court, but it is only competent, when specific requirements are met and the states involved have agreed to its competency. Several ad-hoc courts for specific conflicts were erected and disbanded, when they had fulfilled their function).

Before these treaties, ius ad bellum and ius in bello existed. Ius ad bellum (right to war) regulated, when nations were allowed to declare war (since WWII the Charter generally prohibits the use of force between the members, the only exceptions being self-defence and actions by the Security Council). I'm using "regulated" and "existed" rather liberally, even the existence of international law itself gets disputed. Ius in bello (right at war) regulates, what actions are allowed in a war. They were customary law, and were based on religious beliefs, a sense of morality, virtues, (knightly) honour etc. (Neff, Stephen, War and the Law of Nations – A General History, Cambridge University Press, Cambridge (2005), p 23 and following).

During the 19th century efforts began to codify such rules in Europe. One prominent name in this context is Henry Dunant, who is famous for founding the International Red Cross. He happened on the aftermath of the battle of Solferino in Italy (24 June 1859, France and Sardinia against Austria), and started to look for ways to ease the suffering of the wounded. This lead to peace conferences in Dunant's hometown of Geneva. Which eventually led to the signing of the First Geneva Convention on 22 August 1864 by 12 European powers (among them Prussia and France). It included a few provisions which are now forbidden as war crimes, especially that wounded enemy soldiers may not be executed ("shall be collected and cared for", "shall be repatriated"). It did not call yet explicitly for criminal prosecution, however the signatary states were expected to adhere to the rules (Art 6) and "shall issue instructions to their armed land forces which shall be in conformity" to those rules (Art 1).

1899 several conventions were signed in The Hague, Netherlands. The second one, Convention with respect to the Laws and Customs of War on Land, has a catalogue of what we call now War Crimes, which are still in force - Art 4 - 20 deal with Prisoners of War, Art 23 forbid the execution of surrendered soldiers, the use of weapons with cause superfluous harm, Art 28 forbids pillaging etc.

While the conventions forbid acts, which (from today's perspective) constitute war crimes, and the revision of 1907 called for reparations, they neither used the term war crime nor did they call for criminal prosecution of offenders.

I have no sources available now, in what way the countries dealt with offenders in their armies. The first successful international attempts (the sources I quote mention) to bring war criminals to justice were the Nuremberg and Tokyo tribunals after WWII.

For the Nuremberg Trials, new treaties were signed, namely the Agreement for the prosecution and punishment of the major war criminals of the European Axis. It had an annex ("Charter of the International Military Tribunal"), which defined in Art 6 Crimes against Peace, War Crimes and Crimes against Humanity (which included genocide). Most of the Charter however dealt with how the court was working - numbers of judges, how to conduct the trial, the rights of the defendants to a fair trial and so on. The Tokyo Tribunal had corresponding treaties and rules.

WWII lead to The Convention on the Prevention and Punishment of the Crime of Genocide, Adopted by Resolution 260 (III) A of the United Nations General Assembly was signed on 9 December 1948 and a revision of the Geneva Convention 1949.

The UN Security Council erected specialized courts to deal with war crimes in the Former Yugoslavia in 1993 and Rwanda in 1994, both with specific statutes. Those led to the creation of the International Criminal Court 2002, a permanent international tribunal in The Hague, Netherlands, with the – theoretical – jurisdiction to prosecute individuals for the international crimes of genocide, crimes against humanity, and war crimes, which are also defined there. Although over 120 states have become parties to the Rome Statute of the ICC, others have refused or withdrawn, among them the USA, Russia, India, Israel and China. Further, even for those countries who signed the treaty, the national courts have priority. (I hope it is okay I mention this recent development, although it is just 19 years)

Sources: Shaw Malcolm, International Law, 6th edition, Cambridge University Press, Cambridge 2008

Verdross Alfred (unter Mitarbeit von Stephan Verosta und Karl Zemanek), Völkerrecht, 6. Auflage, Springer, Wien (1964)

Best Geoffrey, War and Law since 1945, Clarendon Press, Oxford (1994)

Satzger Helmut, Internationales und Europäisches Strafrecht, 7. Auflage, Nomos, Baden-Baden (2016)