For years African countries have complained that the International Criminal Court has focused exclusively on African conflicts. In some ways this was unintentional: the court can investigate only atrocities committed after its creation in 2002, and in that period many of the bloodiest conflicts in the court’s jurisdiction have taken place in Africa.

But the African focus shows how tricky the jurisdictional questions are. Much of Africa has ratified the Rome Statute, with notable exceptions like Sudan, Ethiopia and Zimbabwe. In some instances, governments in Africa have referred cases involving rebel groups on their own territory, as in Uganda and the Central African Republic. In others, like the postelection violence in Kenya in 2008, the office of the International Criminal Court prosecutor has used its power to open investigations.

But other situations have escaped the court’s reach. At the bloody end of the civil war in Sri Lanka in 2009, 200,000 civilians were trapped on a beach between government forces and the Tamil Tigers. Tens of thousands are believed to have been killed, but the International Criminal Court has never investigated the case. Sri Lanka is a close ally of China. Charges of crimes in Gaza will never be investigated, international justice experts say, because of the ties between the United States and Israel.

The United States never agreed to be subject to the International Criminal Court because of constitutional issues and worries that its citizens, especially soldiers and spies, could be brought before the tribunal. This is no idle fear, given the human rights scandals that have exploded in Iraq and Afghanistan involving United States personnel. Other countries have rejected it as an unacceptable infringement on their sovereignty.

International justice is also slow and expensive, leading some to question whether it is really worth it. The International Criminal Tribunal for the former Yugoslavia was created in 1993, and it is not expected to wrap up its work until 2014. The Special Court for Sierra Leone, which convicted Mr. Taylor, was created in 2002 and has cost hundreds of millions of dollars, leading many people in that impoverished country to wonder whether the money could have been better spent on development.

Debates have raged for years about whether the court, by closing off a graceful exit, makes dictators more likely to fight to the death. Some question whether it is an effective deterrent of war crimes. The court has run into another problem in Libya: the new government seems intent on prosecuting surviving members of the old leadership itself despite deep concerns about the ability to hold fair trials.

Supporters of the court say it has achieved far more than anyone expected when it was created. “The assumption was the court will take years to come into effect,” said Darryl Robinson, a law professor at Queen’s University in Canada who worked as an adviser to the International Criminal Court’s prosecutor. “And once it is in force it is going to be this court with jurisdiction over Canada and Norway, with nothing to investigate.”