The development of transportation systems has significantly enhanced the welfare and modernization of society. Wooden vehicles pulled by animals have been used for land transportation since the early Bronze Age. Whole-body gharries with rigid wheels pulled by oxen appeared in Crete by 2000 BC or earlier. Horses originating from the East were depicted in early Cretan seal-rings of the same period. The two-wheeled horse-drawn chariot was one of the most important inventions in history. This vehicle provided humanity its first concept of personal transport and was the key technology of war for 2000 years. Chariots of Mycenaean and Archaic Greece with light and flexible four-spoked wheels acting as spring suspensions were depicted in vase paintings. The development of this vehicle incorporated the seeds of a primitive design activity and was important for engineering. The Trojan horse since 1194 BC and the helepolis since 700 BC were the first known machines on a wheeled base transported by horses or self-powered. Ancient engineers invented bearings lubricated with fat, and Romans introduced the ancestors of ball bearings for their wagons and carts. The historic evolution of wheeled transportation systems, along with early traction, suspension, and braking systems, is presented in this paper. Analytical and numerical methods are incorporated to analyze the most conceivable loading situations of typically reconstructed wheeled transportation systems in ancient times. Traction requirements both for horse-driven machines and the power for internal motors are also analyzed. This study can serve as a basis for further development of detailed reconstruction of transportation systems in antiquity.