In this talk, I will introduce the regularity of the free boundary for the obstacle problems. First, I will briefly introduce the method blowup and the idea considering the upper obstacle as a solution single obstacle problem. Then, I will introduce the regularity of the free boundary for the double obstacle problems. Precisely, I am going to introduce the proof of local C¹ regularity of free boundaries for the elliptic double obstacle problem with an upper obstacle ψ,