Reykjavík’s most attention-seeking building is the immense concrete church Hallgrímskirkja, star of a thousand postcards and visible from 20km away. However, in a scandal that shook the city, it was discovered that the original builders cut corners by skimping on quality materials, and that Reykjavík’s iconic symbol was falling apart. The whole thing was just repaired. You can get an unmissable view of the city by taking an elevator trip up the 75m-high tower.