The first comprehensive census in Iceland was taken in 1703, at which time 50,358 people were reported. The 18th century was marked by great economic hardship, and by 1801 the population had declined to 47,240. There began a slow increase in the 19th century, and by 1901 the population had risen to 78,470.During World War II and the early postwar time there was rapid improvement in the standard of living and a new acceleration in the rate of population growth. The annual growth rate reached its peak during the 1950s; it has been declining since 1960, primarily because of a sharply reduced birth rate and continued emigration. For a brief time from the late 1980s to the mid-1990s the birth rate rose again before resuming its downward trend. In the late 1980s the population reached a quarter of a million.

Most Icelandic surnames are based on patronymy, or the adoption of the father's first given name. For example, Magnus and Anna, children of a man named Petur, would hold the surname Petursson and Petursdottir, respectively. Magnus' children, in turn, would inherit the surname Magnusson, while Anna's children would claim their father's first given name as their surname. Women normally maintain their original surnames after marriage. This system of surnames is required by law, except for the descendants of those who had acquired family names before 1913. Most Icelanders, while reserved by nature, rarely call each other by their surnames, and even phone directories are based on first names. Because of its small size and relative homogeneity, Iceland holds all the characteristics of a very close-knit society.