Abstract: This talk is self contained but mixes informally math, stat and philosophy of science.I will briefly motivate why Bayesian Analysis is so attractive except for the problem of choice of prior by elicitation of prior belief or algorithmic constructions of objective priors, and then concentrate on the topic described in the title.

I will present relatively new constructions and theorems as well as old criticisms of objective priors and recent answers . I will also explain new criticisms coming from philosophers of science which suggest new open problems.

(This talk is aimed at a general audience.)