For the most part, anyone that commits a crime will be tried for that crime based on the legal system of the country that they reside in at this current point in time. However, sometimes a situation will be so severe and will have such widespread implications that it will become really important to try them in a court that is not bound by any kind of corruption nor would it involve something that might end up making the world a worse place than it currently is without a shadow of a doubt.
As a result of the fact that this is the case, certain cases are only tried in an international criminal court. This court is basically there so that war crimes can be tried,
with the main contributing factor to this b eing that if a state or government ends up being involved in a war crime then it is highly unlikely that courts in their own country would be willing to sentence them. Hence, the only way in which true justice can be served is if the case is tried in a court that is absolutely impartial and would not give deference to anyone at all based on the kinds of political connections that they might have.
Suffice it to say that the world needs an international court where such cases can end up being tried. Without such a court, most individuals that are in a position of reasonable power would find that they can whatever they like without having to suffer any major consequences along the way, and this can truly destabilize the world and push us back a few centuries in terms of social progress and innovation.