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I will present a series of far-reaching new existence and structure results for convex ancientÌýsolutions to mean curvature flow. An interesting picture (conjectured by Huisken and Sinestrari) emerges:Ìýconvex ancient and translating solutions in slab regions decompose into certain canonical configurations ofÌýGrim Reapers, subject to certain necessary constraints. In particular, we construct new families of solutionsÌýwith discrete symmetries as well as families of solutions which possess only a single reflection symmetry.ÌýThese include many eternal solutions which do not evolve by translation (resolving a conjecture of White inÌýthe negative). Prior to these results, the only known examples were the rotationally symmetric ancientÌýpancake and the rotationally symmetric flying wing translators. Several interesting questions remain open,Ìýhowever. This is joint work with Theodora Bourni and Giuseppe Tinaglia.