In their seminal paper, Eliashberg and Polterovich introduced a natural bi-invariant relation on the universal cover of the contactomorphism group of a closed contact manifold.

Depending on the contact manifold, this relation can be either a partial order (the contact manifold is "orderable") or trivial.

In this talk we will discuss a connection between orderability and the diameter of the group of contactomorphisms with respect to the contact analogue of the Hofer norm.

In particular we will see examples of contact manifolds with infinite and such with finite contact Hofer diameter.

Moreover we will discuss how the contact Hofer norm can be used to prove new criteria for non-orderability in terms of open book decompositions.

This talk is based on a joint project in progress with Egor Shelukhin.