This will be the subject of International law and Treaties. EU law only comes in when it concerns purely EU citizens (please note: EU citizens). This is because if there is a request by a non-EU country to extradite an EU citizen, the EU citizen may claim the protection of the Member State he is in, if that Member State has in place laws forbidding extradition of their own nationals. If the Member State does not have such a law, then this will not apply (See the Case Petruhhin). However many EU Member States forbid extradition.Now, extradition plays a different role if a criminal has been sentenced and has fled and the country which has sentenced him is requesting extradition for his imprisonment.See this paper for more info: Extradition to non-EU countries: the limits imposed by EU citizenship