A German court has convicted John Demjanjuk of participating in the murder of more than 28,000 Jews at World War II death camps. The 91-year-old, who for years fought deportation from the United States, faces five years in prison. Now that Demjanjuk has been sentenced, how many Nazi war criminals are still at large?

Probably hundreds. The Simon Wiesenthal Center, a Jewish human rights group based in Los Angeles, publishes an annual report on the investigation, indictment, extradition, denaturalization, and conviction of Nazi war criminals worldwide. In their last full report (PDF), released in November 2010 and covering the period ending March 31, 2010, they noted that there were 852 ongoing investigations of accused Nazis. While that’s probably the best number available, it’s a very rough estimate. Some of the investigations involve multiple suspects, although the reporting governments won’t say which or how many. Several countries declined to respond to the center’s request for information, while others refuse to investigate World War II-era crimes as a matter of policy. (For example, the statute of limitations applies to murder—and even, until recently, to genocide—in Sweden and Norway, precluding any punishment for Nazi war criminals.) That means there are an unknown number of former Nazi executioners living anonymously around the world.

On the other hand, there are probably some innocents under investigation. Prosecutors have opened 2,718 investigations globally since the beginning of 2001, but have only achieved 87 convictions. While some of the remaining 2,631 cases are ongoing and many suspects have died, prosecutors have also dropped a large number for lack of evidence.

Even among those countries that are officially willing to investigate Nazi war crimes, some are more serious about it than others. Poland leads the world in open cases with 316, and Germany has 177. (Many of these are quite new. Between April 1, 2009 and March 21, 2010, German prosecutors opened 130 new cases.) Meanwhile, Austria—Germany’s neighbor to the south and most likely the home of a fair number of former Nazi genocide practitioners—has just 28 investigations ongoing. The country hasn’t convicted a Nazi war criminal for more than 30 years. Austria did, however, establish a commission recently to investigate Nazi war crimes allegations.

As for the United States: There were 87 open investigations as of April 2010. And one of the Simon Wiesenthal Center’s most wanted war criminals, a Michigan man named Ivan (John) Kalymon, has been stripped of his citizenship and awaits deportation.

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Explainer thanks Efraim Zuroff of the Simon Wiesenthal Center and author of Operation Last Chance: One Man’s Quest to Bring Nazi Criminals to Justice.