The amplituhedron A(n,k,m) is a geometric object that encodes scattering amplitudes in various quantum field theories. It has been studied since its discovery in 2013 by Arkani-Hamed and Trnka. One of the central conjectures about it has been that a certain collection of simpler subspaces forms a tiling of the amplituhedron A(n,k,4). In joint work with Tsviqa Lakrec and Ran Tessler, we have settled this conjecture. In the talk, I will define the amplituhedron, discuss the tiling problem, present the combinatorial structures that appear in its solution, and outline the main ideas from the proof.