Short answers, pulled from the story.
84 American prisoners of war were murdered by Waffen-SS troops. This event illustrates a core category of war crimes involving intentionally killing civilians or combatants who have surrendered.
Peter von Hagenbach became the first person tried for a war crime in 1474 before an ad hoc tribunal of the Holy Roman Empire. He was convicted and beheaded despite claiming he had obeyed superior orders because he failed to prevent criminal behavior by his soldiers.
Franz Lieber wrote this document to define command responsibility for war crimes committed by Union Army soldiers fighting Confederate forces. The Lieber Code appeared as General Order 100 on the 24th of April 1863 during the American Civil War.
The International Criminal Court came into being on the 1st of July 2002 located in The Hague for prosecuting war crimes committed from that date forward. Article 12 of the Rome Statute provides jurisdiction over citizens of non-contracting states if they commit crimes within territory belonging to state parties.
Russian President Vladimir Putin faces charges for illegal abduction of children from Ukraine during the invasion beginning in February 2022. These actions constitute violations under international humanitarian law definitions of war crimes.