The pocket square made its first appearance in ancient Egypt, in the heyday of the first world power. It was however not the pocket square as we know it today. It had a more utilitarian function as a white linen handkerchief. Then it disappeared on the succeeding world powers which were more preoccupied with military pursuits and staying in power. It had a resurgence in Ancient Greece who, like the Ancient Egyptians, had a penchant for culture. The Greeks picked up the white linen handkerchief from the Egyptians which became part of its empire.
The linen handkerchief as a phase stayed for a long time. In fact, it was not until the turn of the 20th century that the pocket square came on its own. What actually happened was the pocket square forked from the utilitarian handkerchief to solely become a fashion accessory. The handkerchief has stayed around although suffering from intense competition from tissue paper.
The pocket square was initially placed in the trouser pocket. But with the advent of the two-piece suit in the 19th century, it found a better vantage point in the coat's pocket, out front. Displayed in such a prime location, the pocket square blossomed into the sheer number of patterns and designs it had been made in. Matching the tie or bow tie, it was made in the floral pattern that dates back to ancient Egypt, in the checkered pattern that came from chess (yes, that’s true), in Paisley, a curved teardrop motif from Persia...in fact in every major popular pattern in the fashion industry today. For formal occasions, it took on satin which is traced back to ancient China through the Silk Road that reached Western Europe.
There was actually a convenient reason for having the pocket square in the patterns of ties and bow ties - the pocket squares had to match. You see, when the pocket square found its way into the coat's front pocket, it did so as an accent - a companion - either to a tie or to a bow tie. So to match the tie or bow tie, it had to be in the themes, designs, and patterns of the neckwears it accented. For a time, the pocket square was just an accent.
Then around the time that the popularity of the tie waned, the fashion Avante-garde realized that they can ditch the tie or bow tie for a more on-the-edge look, but still wear a pocket square as the crown-jewel of their attire. That's was when the pocket square truly came on its own.
The pocket square has developed so much, it now has it's own fashion accessories - like the pocket square wallet - as well as iterations. The pocket round came into being from the floral folds invented on the pocket square. The pocket round can be stuffed in the coat's pocket much like a reverse puff fold for a pocket square, and you have a proverbial cornerless flower on your front pocket.