A survey on the Hausdorff dimension of intersections

Let $A$ and $B$ be Borel subsets of the Euclidean $n$-space with $\dim A+\dim B>n$. This is a survey on the question: what can we say about the Hausdorff dimension of the intersections $A\cap (g(B)+z)$ for generic orthogonal transformations $g$ and translations by $z$.