The Zodiac is believed to have developed in ancient Egypt and later adopted by the Babylonians. Early astrologers knew it took 12 lunar cycles (months) for the sun to return to its original position. They then identified 12 constellations that they observed to be linked to the progressions of the seasons and assigned them names of certain animals and persons. The signs of the Zodiac are sub-divided into four groups:
Fire Signs: Aries, Sagittarius, Leo
Water Signs: Cancer, Scorpio, Pisces
Air Signs: Libra, Aquarius, Gemini
Earth Signs: Capricorn, Taurus, Virgo
In Ancient and Traditional times there were only a few crystals allocated to each sign, but as time has gone on and more crystals have been found these lists have become more intense. These days I believe it is not about the crystal allocated to your star sign, but more about the crystal you need at the time. If you are buying as a gift for someone then by all means, go by signs. If you are buying for yourself choose by intention and what it is you want your chosen crystal to do for you.