A matter of jurisdiction
<p>As far as I know there are countries with extraterritorial jurisdiction when it comes to protect their citizens, so in the latter's favour. 
If for example a PR of Italy beats up and injures severely a tourist from the US visiting Italy, to the point of causing them massive physical damage, and the perpetrator is caught, which istitutions would the case be assigned to, Italian or US courts???</p>

<p>Has it happened  in any istance that a criminal has been sent to a foreign country to attend the court for a crime he has committed against that country's citizen, even though the criminal's never been in that country itself?</p>

<p>Generally, extraterritorial jurisdiction acts as a backup. If the Italian courts want to prosecute, the US will not claim jurisdiction. And if the Italians do not want to prosecute, they're unlikely to extradite the "offender" either.</p>

<p>Now for physical crimes the location of the act makes it generally obvious which jurisdiction takes precedence, but for online crimes this can be less transparent. but a country that has arrested the offender and wants to try the crime probably still gets precedence.</p>

<p>Extraterritorial jurisdiction will come into play only for certain citizens in other countries.  For example, military personnel stationed in another ally's country may or may not be subject to local law for all offenses.  This will be set by agreement between the two nations.</p>

<p>There are certainly laws that apply to US citizens even when they are abroad.  There are also US laws that are used to enforce anti-terrorism measures across the globe, though that enforcement is generally via military might.  However, there are no laws that affect foreign nationals in their home countries for normal criminal offenses.  Moreover, very few sovereign nations would allow a foreign court authority over their citizens for events that occur within its borders.  In your example, the only jurisdiction is the appropriate one in Italy.</p>

<p>It is possible that there have been instances of defendants being sent outside of a country for trial, but this would be a diplomatic solution, not a jurisdictional one.</p>

multiple-jurisdiction