Archaeological records provide examples of ways shoes were fastened to the foot, although finding footwear samples proves difficult due to shoes and laces being made of natural materials that deteriorate quickly. The earliest known example of a laced-up closed-toe shoe is the 3500 BC Areni-1, a 2008 discovery in Armenia by post-graduate student Diana Zardaryan:
Simple pieces of leather were bound to the foot and ankle with laces in 2000 B.C. during ancient Mesopotamians times. Ancient Greeks wore sandals with rawhide lacing. Roman soldiers popularized the use of shoes, and therefore lacing, to Western Europe. This photo demonstrates a modern reproduction of the Roman soldier laced shoe:
In the Museum of London, there is an example of laced medieval footwear from the 12th century. This historical document shows a shoe with lacing down the front and side of the shoe through a series of hooks.
Some historical records suggest that the shoelace with aglets was invented in England on March 27, 1790 by a gentleman named Harvey Kennedy. The fashion of the time was to adorn ones shoes with highly embellished buckles, so Mr. Kennedy perhaps sought a more practical option. However, this contemporary iteration of agleted shoelaces we all know and love did not become widely popular until the 20th century. Here you can see a Victorian era example: