In [Invent. Math. 217, 35–76 (2019; Zbl 1414.53059)], the authors of the paper under review prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in \(\mathbb{R}^3\) which is strictly convex and non-collapsed. In the paper under review, using similar techniques, the authors classify all noncompact ancient solutions to mean curvature flow in \(\mathbb{R}^{n+1}\), \(n\geq 3\), which are convex, uniformly two-convex, and non-collapsed, proving that such an ancient solution is a rotationally symmetric translating soliton. As a direct consequence, the following interesting result is derived: Let us consider an arbitrary closed, embedded, two-convex hypersurface in \(\mathbb{R}^{n+1}\), and evolve it by mean curvature flow. Then it follows that, at the first singular time, the only possible blow-up limits are shrinking round spheres, shrinking round cylinders, and the unique rotationally symmetric translating soliton.