Advanced polymer-based composite materials have revolutionized the structural material arena since their appearance some 60 years ago. Yet, despite their relatively short existence, they seem to be taken for granted as if they have always been there. One of the reasons for this state of affairs is that composite materials of various types have accompanied human history for thousands years, and their emergence in the modern era could be considered a natural evolutionary process. Nevertheless, the continuous line that leads from early days of composites in human history to current structural materials has exhibited a number of notable steps, each generating an abrupt advance toward the contemporary new science of composite materials. In this paper, I review and discuss the history of composites with emphasis on the main steps of their development.