TITLE: What are the main open problems in the theory of amenability of groups?
QUESTION [16 upvotes]: I have read the Paterson and Runde books about amenability of groups, but I do not know what are the most intriguing questions in this area today.
A survey or a list of questions would be welcome.

REPLY [3 votes]: The Part C of Appendices of the book "Amenability of discrete groups by examples"
by Kate Juschenko, contains open problems in amenability.