How much a biLipschitz map can spiral? We explore two complementary aspects: how fast and how often. Quasiconformal techniques turn out to be effective to study this problem. In many ways, rotational phenomena for biLipschitz maps are dual to stretching properties of quasiconformal maps. I will contrast these two and explain what links them together.

The talk is based on joint work with K. Astala, T. Iwaniec and E. Saksman.