The minimal log discrepancy introduced by Shokurov is a basic invariant in birational geometry. Shokurov conjectured that the set of minimal log discrepancies should satisfy the ascending chain condition. This conjecture has a close relation with the termination of flips in the minimal model program. In this talk, I will show that Shokurov's conjecture holds for terminal threefolds. Some applications will also be discussed. This is a joint work with Jihao Liu and Yujie Luo.