Projection Theorems and Applications

Given a fractal set E in $R^n$ and a set F in $Gr(k,n)$, can we find k-plane S in F such that the orthogonal projection of E onto S is large?

We will survey some classical and recent projection theorems and discuss their applications.  This is based on joint works with Gan, Guo, Guth, Harris, Maldague, Orponen, and Shmerkin,