They are horn worms but this one is in its final instar and has shed the horn leaving an 'eyespot'. They feed on grape, Virginia creeper, and woodbine. The mature caterpillar is two or more inches in length, and the adult moth's wings can span your palm. The adult, like most hawk moths, feeds at night, sipping from flowers, pollinating as they go.
When disturbed, the caterpillar can retract its entire head. (bottom photo)