Iceland has widespread 4G coverage at competitive prices.
Iceland is part of an EU/EFTA trade agreement which means data, SMS and phone call pricing is the same for people traveling within the European Economic Area.
Compare plans at Aurbjörg. Some companies offer a bundle deal with home internet.
If you need prepaid only SIM card, Síminn and Vodafone provide this. You can get prepaid without a kennitala.
Most homes in Iceland have access to high-speed fibre optic internet. Depending on your provider, you may pay a separate line-rental charge for the fibre cable in addition to the Internet service charge. Some providers bundle this cost, so check this when comparing prices.