Insurmountable Hubble tension

Using the most recent available cosmological datasets the Hubble tension has climbed to beyond 7 sigma significance. Different families of measurements point towards two hardening camps, and in this talk I review the efforts of the H0DN collaboration on testing the consistency of local measurements, outlining the lessons learned from this systematic audit. With the tension increasingly appearing insurmountable to reconcile, I discuss what models beyond LambdaCDM still offer any hope at resolving the puzzle and how they work in detail and the prospects we have for further disambiguating between them.