Skatturinn
The Iceland Revenue and Customs (Ríkisskattstjóri) is in charge of tax and customs and manages an institution called Skatturinn. The agency handles taxation, customs duties and other fees.
Further information: https://www.skatturinn.is/english/
Information about filing a tax return in English: https://www.rsk.is/media/baeklingar/rsk_0812_2020.en.pdf