If you are not from the EEA or EFTA, the employer who wants to hire you applies for a work permit at the Directorate of Immigration (Útlendingastofnun, say: OOT-len-din-ga-stof-nun, the office for foreigners). If the residence rules are met, the file goes to the Directorate of Labour (Vinnumálastofnun, say: VIN-nu-mowl-a-stof-nun, the state work office), which gives the work permit. A work permit alone does not let you live here. You need a residence permit too. Citizens of the EEA and EFTA can move here freely and need no permit. (EEA means the EU countries plus Iceland, Norway and Liechtenstein. EFTA is Iceland, Norway, Switzerland and Liechtenstein.)