Kópavogur is one of the youngest towns in Iceland so there is not much there of historical significance. It was a suburb of Reykjavík with the first houses built during WW2. Recent post 1990 explosive growth in both business and housing building doubled the town in size, giving it large shopping centers and an office/commercial building that is the tallest building in Iceland but the things to see are primarily in the older part of the town, particularily the Kársnes peninsula with trees in the gardens and treelined streets and the picturesque church on top of the Borgarholt.