Three different UN bodies are now tasked with answering the question:
Have war crimes been committed during the war in Ukraine?
It is not entirely easy to keep the three processes separate, so here is a brief summary:
International Criminal Court, ICC
The court has the task of prosecuting people for genocide, crimes against humanity and war crimes.
It is currently investigating whether something like this happened during the war in Ukraine, and who is responsible in such cases.
The court thus does not prosecute states but individuals, such as soldiers, commanders or decision-makers.
Russian President Vladimir Putin could theoretically be convicted here, but Russia has not approved the court, which thus has no jurisdiction in the country.
The ICC can issue an arrest warrant against people, and even sentence them to punishment like a regular court.
International Court of Justice in The Hague, ICJ
The court decides disputes between states, for example regarding the Convention on Genocide.
It is currently being investigated whether Ukraine carried out genocide on Russians, which was the reason Russia stated when they began the invasion of the country.
No individuals can be investigated here, only states.
The legal process, which was started by Ukraine, is thus about the country wanting to prove that they did not commit genocide.
However, when the hearing began with Ukraine's presentation on Monday, Russia's representatives never showed up.
On Tuesday, it is thought that Russia will be allowed to respond to Ukraine's arguments.
If this happens, Russia could be sentenced to apologize for the allegations.
However, the court does not investigate whether the invasion is legal, and Russia can not be forced to withdraw its troops.
UN Human Rights Council, UNHRC
The UNHRC (not to be confused with the UN refugee agency UNHCR) is not a court and thus no legal process is ongoing.
However, the Council has voted to appoint a commission of inquiry to investigate crimes committed against humanity during the war in Ukraine.
The Council has no possibility of imposing penalties or sanctions, but a statement from the Council can be seen as a clear diplomatic signal.
It is also common for such an investigation to form an important part of a court process in the ICJ or ICC.