Positive loops of contactomorphisms

In 2000 Eliashberg-Polterovich introduced the notion of positive contact isotopies and studied induced biinvariant partial orders on contactomorphism groups. In 2006 Eliashberg-Kim-Polterovich discovered a link to contact (non-)squeezing. At the core of these works are so-called (contractible) positive loops of contactomorphisms. Existence of or obstructions to (contractible) positive loops are difficult questions. In my talk I will explain basic notions and give simple examples illustrating these. Towards the I will explain some results concerning obstructions and a link to the famous Weinstein conjecture.