This introductory chapter explains about the phenomenon of sustained low fertility for the non-specialist reader – from a consideration of the possible demographic repercussions of low fertility to the history of the (two) demographic declines in Europe. It discusses the convergences and divergences in reproductive patterns and behaviour across Europe at the beginning of the twenty-first century. Shrinking” populations, or negative population growth, is one expected consequence of low fertility. After twenty or more years of below replacement level fertility, deaths now exceed births. The chapter describes the History of Demographic Perspectives. Investigation into the causes of the demographic transition brought to light characteristics of European fertility. According to demographers, there were two main components of the decline. One, called the Malthusian transition after Thomas Malthus, was delay and/or curtailment of marriage. The second demographic transition was the label demographers gave to the phenomenon of “continuing fertility decline beyond the end of the (first) demographic transition to levels below replacement.