There’s a lot to be said for Jonah’s very practical answer, but the
more legalistic response is that foreigners are answerable to U.S. law
for various crimes committed overseas against what Congress, subject to
the (pretty tiny) limitations of the Constitution, deems are American
interests. The easiest examples are probably terrorist acts which
target American persons or property. Mohammed Daoud al-`Owhali, for
example, bombed the U.S. embassy in Nairobi. He was a Saudi pretending
to be a Yemeni whose crime (and arrest) took place in Kenya, who had
never set foot in the U.S., and whose only connection to the U.S. was to
have attacked that American installation. He was surrendered by Kenya
to the U.S., convicted of various U.S. terrorism crimes, and is serving
a life sentence (having convinced the jury not to impose the death penalty).
Most matters of national security concern, like espionage, are
analogous. They involve U.S. assets — in the case of espionage, not
persons or defense facilities but information that is vital to U.S.
national security. Consequently, it presents no Constitutional problem
for Congress to write laws that reach such conduct committed outside
U.S. territory. Similarly, drug traffickers who participate in
exporting drugs to the U.S. (e.g., Noriega) or laundering drug money (or
other known criminal proceeds) from the U.S. are chargeable under
American law. Foreign companies who trade on our exchanges can be
reached if they commit a fraud overseas that has American consequences.
Usually, the more interesting problem — as Jonah suggests — is
getting your hands on the bad guy. Other countries are not always crazy
about the elastic reach of our laws. So sometimes they will refuse to
extradite. Or they will extradite with conditions (e.g., the European
countries generally won’t turn over even terrorists unless we agree not
to seek the death penalty; the head of the Sicilian Mafia — who was the
lead defendant in the famous Pizza Connection case in the 1980’s —
faced a limit of 30 years in jail because he was captured in Spain,
where the maximum penalty for any drug crime was 30 years, and Spain
would not extradite unless we promised to honor that cap).
The other thing foreign countries will sometimes do to thwart us is
charge under their own laws the defendants we want them to extradite to
the U.S.. At first blush, this sounds like it would be helpful to U.S.
law enforcement, but it is decidedly not. This is because most European
countries (a) have far more lenient penalties than we do and (b) adhere
to the double jeopardy principle of “ne bis in idem” — which
essentially means they will not extradite for any U.S. crime in which
any part of the evidence involves something they’ve already charged
themselves. Thus, for example, a Dutch CEO who commits a securities
violation for which he might be looking at 20 or more years in the U.S.
but only a year or so in the Netherlands benefits greatly from being
charged there. Ditto the Germans who participated in the 9/11 attacks
and whose maximum sentence, under German law, was 15 years even though
their conduct involved 3000 homicides.