People had been living in Hesteyri from the settlement times. Most of the time it was the home of just a few farmers and fishermen. It wasn't a particularly busy place until Norwegian whalers built a factory there in 1890 along with harbors and dwellings for workers. Hesteyri became an active community with a school, shop and a church. At its busiest time the population was around a hundred.
Whaling ban was put on in 1915 and the factory closed down. Quiet times didn't last long. Entrepreneurs from Reykjavik bought it and converted into a herring factory. It operated as such until 1940 when the herring disappeared. The factory closed down for good. In 1952 there were only 30 people left in Hesteyri. In the spring they had a meeting in the community house to figure out what to do about the situation. On that meeting they decided to leave Hesteyri all together the following autumn. Since November that year nobody has lived there.