The restriction conjecture, one of the central open problems in Fourier analysis, asks how the Fourier transform of a function supported on a curved surface like the sphere can be controlled in terms of the surface's curvature. Hong Wang, of IHES and NYU, surveys the state of this problem at the Institute for Advanced Study, tracing its history from the Stein-Tomas theorem through more recent progress tied to the Kakeya conjecture and incidence geometry. She lays out the main conjectures in two and higher dimensions, the tools that have driven recent breakthroughs, including polynomial partitioning and decoupling methods, and the gaps that remain unresolved. The talk is pitched at a research audience familiar with harmonic analysis, moving through technical machinery while keeping the overall landscape of the field visible. It gives a working mathematician's map of where the restriction problem stands and what the open questions actually are.