There are no written records that definitely pinpoint when or where the tradition of Christmas stockings originated but the tradition is very old, probably originating from the Germanic/Scandinavian figure "Odin" when children would fill their boots with carrots, straw, and sugary treats, near the hearth for Odin's flying horse, "Sleipnir". As a reward, Odin would replace the horse's food with gifts and candy.
Over time the practice became associated with Saint Nicholas or Santa Claus. Traditions of some countries vary. In France children place their shoes by the fireplace. Italian children set their shoes out on January 5th, the night before Epiphany. Children of Holland place wooden shoes at the hearth, and in Puerto Rico, children leave gifts in small boxes filled with flowers and foliage for the camels of the Three Kings.
Many families create their own unique Christmas stockings which live on to become treasured hand-me downs or keepsakes. These stocking images provide great patterns for home-made fire-place mantel or hearth decorations. We generally place our stockings next to the tree for safety sake, due to the danger of fire, plus the heat of a fireplace tends to melt chocolate. I've not heard any complaints from Santa yet.