Short answers, pulled from the story.
Peter von Hagenbach was the first person in recorded history to be tried for a war crime. He stood before an ad hoc tribunal of the Holy Roman Empire in the year 1474 and was convicted and beheaded for allowing his soldiers to massacre civilians in the town of Brisach.
President Abraham Lincoln issued General Order 100, known as the Lieber Code, on the 24th of April 1863. The document was written by Franz Lieber, a German lawyer and veteran of the Napoleonic Wars, to define command responsibility and outline the military responsibilities of Union soldiers.
The Nuremberg trials were based on the London Charter published on the 8th of August 1945. The Tokyo War Crimes Tribunal was convened on the 3rd of May 1946 to try the leaders of the Empire of Japan for crimes against peace, war crimes, and crimes against humanity.
The International Criminal Court came into being on the 1st of July 2002. It has jurisdiction over war crimes committed on or after that date when they are part of a plan or policy or as part of a large-scale commission of such crimes.
The International Criminal Court has prosecuted prominent figures including Vladimir Putin and Benjamin Netanyahu for their alleged involvement in war crimes. The court also targets current leaders and has indicted former heads of state like Omar al-Bashir and Charles G. Taylor.