Abstract: The double-bubble theorem in 3D is an extension of the isoperimetric inequality. Motivated by Plateau’s laws of surface tension it states that among the shapes consisting of two disjoint sets (possibly sharing boundary) with given volumes, the shape which minimizes area is the union of two spheres meeting at an angle of 120 degrees along a common circle, like observed in soap bubbles. A remarkable generalization of the theorem was conjectured by Sullivan, for multi-bubbles in higher dimension. Recent breakthroughs by Emanuel Milman and Joe Neeman have resolved the double, triple, and quadruple bubble cases in higher dimensions, confirming Sullivan’s conjecture in these instances. I will discuss some of the ideas underlying their proofs.