Ancient solutions appear as singularity models of mean curvature flow. In this talk, I will discuss the classification of bubble-sheet ovals in $\mathbb{R}^{4}$ based on my joint work with Beomjun Choi, Toti Daskalopoulos, Robert Haslhofer and Natasa Sesum. Bubble-sheet ovals are ancient noncollapsed solutions of mean curvature flow whose tangent flow at $-\infty$ is $ \mathbb{R}^{2}\times S^1$ and which have inward quadratic bending asymptotics. We prove that they belong to either the O(2)×O(2)-symmetric ancient oval constructed by White as well as Haslhofer-Hershkovits, or belong to the one-parameter family of Z_2^2×O(2)-symmetric ancient ovals constructed by Robert Haslhofer and myself.