Whats wrong with the Platonic ideal of space and time?

This is a chapter for an upcoming book, Space, Time, and the Limits of Human Understanding, edited by Shyam Wuppuluri and Giancarlo Ghirardi. I first present the classical picture of flat space and ever-flowing time, as generally accepted until about 1900, discuss the challenges posed by modern physics and the adjustments required by special relativity, general relativity and quantum mechanics, and finally consider (and reject) a recent hypothesis that space-time is essentially discrete. Ultimately, none of the simple answers to what is space-time? stand up to reality. We have more work ahead of us!