There are a number of housing issues that need consideration, including domiciliary registration, entitlements and obligations in relation to property purchases and rentals of housing, such as interest benefits and housing benefit.
Further information: https://island.is/flokkur/husnaedismal
The Housing and Construction Authority (Húsnæðis- og mannvirkjastofnun, HMS) takes decisions regarding entitlement to housing benefit. Housing benefit takes the form of monthly payments intended to assist those who rent residential premises, whether this is within the socially-assisted housing system, in student residences or on the open rental market.
On the HMS website you can apply for housing benefit and calculate housing benefit amounts. Further information: https://www.hms.is/husnaedisbaetur/housing-benefit/