Ax proved a functional analogue of Schanuel's conjecture in 1971. I will show how one can use it to axiomatise the first-order theory of the exponential differential equation in analogy with Zilber's pseudo-exponentiation. Then I will discuss the possibility of Ax-Schanuel type results for other functions (differential equations), and some related problems. If time permits, I will show how Ax-Schanuel can be applied to prove a weak version of the Conjecture on Intersections with Tori.