There is good literary evidence that geared models, displays or calculators of the motion of the heavens (including planets) existed and were widely known about during the period about c250 BCE to 500 CE. The Antikythera Mechanism is the only surviving example. I will argue that such mechanisms were very important in the development of astronomical and philosophical views. I will follow the faint trail left by similar devices until about 1300 AD when the technology had a spectacular and sudden re-appearance in Western Europe. The continuing influence of mechanical models will be followed through the "Scientific Revolution" and on into the 20th Century. I will speculate on whether the advent of quantum mechanics has made such models no longer useful.