Iceland was one of the last places in Europe to be settled. It thus has a relatively short population history as it was completely depopulated until about 871. Harsh climatic conditions, periodic epidemics, and numerous natural disasters were not conducive to robust population growth on the island. This article traces the demographic transition of Iceland’s population from the initial settlement to the present. This is the transition from high to low birth and death rates as a population modernises. Iceland has an impressive literary and historical record-keeping tradition beginning with the Saga Age in the 900s. It also has long had a well-developed statistical system which allows the study of population trends much further back in time than many countries. The results show slow population growth for much of Iceland’s history with many episodes of steep population decline. A series of technological innovations in the 19th century allowed the country to modernise, the population to grow, and its demographic situation to improve. Iceland has completed the demographic transition, the population is growing, in part due to high immigration, and it has some of the best demographic indicators in the world. Despite these favourable trends, the country faces some demographic challenges.