As Amanda from SG has reminded me, Joe Polchinski participated at the Solvay Conference and gave an interesting talk about the cosmological constant and the string landscape that you can now see in the written form. I think that he defines very well what the problem is - more precisely, what the three problems are - and what are the two basic categories of explanations of the value of the cosmological constant. I would call these two categories “genuine explanations” and “non-explanations”, but it is a matter of terminology. Many readers consider Joe’s review to be the best available defense of the anthropic reasoning.
The paper is recommended especially to everyone who thinks that the cosmological constant problem is an easy problem. Joe shows how the loops contributing to the Lamb shift couple to soft gravitons which is why you can’t declare the short-distance physics “absent”. Our colleagues who are experts in numerology will surely try to explain why
vacuum energy = exp (-283.2) Mplanck^4
Where does the number 283.2 come from?