The Geneva Conventions and Protocol 1 describe what they call ‘grave breaches’ of international humanitarian law, and both Ukraine and Russia are parties to these treaties.
Grave breaches include directly attacking civilians and launching an indiscriminate attack affecting the civilian population or civilian property.
Many states and the International Criminal Court (ICC) also have the possibility to prosecute a wider set of war crimes although, in the past, states have not prosecuted many such crimes committed outside their own territory.
Neither Russia nor Ukraine is a party to the ICC Statute, but Ukraine did declared it accepted the Court’s jurisdiction for crimes on its territory, and and investigations have now started.
But there are several problems to be overcome to achieve successful prosecutions, such as the collection and preservation of evidence, proof of the intent of the suspects in the heat of war, how to be arrest suspects, and the issue of immunity.