Hong Wang, mathematician at New York University, delivers this Emmy Noether Lecture at the Institute for Advanced Study on projection theory, the study of how the Hausdorff dimension of a set in R^n behaves when projected onto lower-dimensional subspaces. Wang surveys both orthogonal projections and more general nonlinear projection families, focusing on when dimension is preserved and how to bound the exceptional set of directions where it degrades. The talk traces the discretized, multi-scale approach to these problems pioneered by Bourgain and extended by Shmerkin and Orponen, showing how finding structure inside an arbitrary subset of R^n leads to sharper projection estimates. Delivered at Simonyi Hall 101, the lecture is aimed at an audience with background in geometric measure theory and harmonic analysis, and surveys recent progress rather than a single new result.