Fly tying for fly fishing has not changed significantly since the mid 1800s with the exception of the introduction of synthetic materials and updated hook designs.
Though there is a huge variation in fly design, the driving theory behind them all, of course, is to cause the desired species of fish to attack the fly. David Hughes described 4 categories of fly design in Trout Flies - The Tier's Reference, including Searching, Impressionistic, Suggestive, and Imitative.