Selection Principles and special sets of reals: Open problems

We give a selection of major open problems involving selective properties, diagonalizations, and covering properties for sets of real numbers. This is a revision of the version published as a chapter in the book \textbf{Open Problems in Topology II} (E. Pearl, ed.), Elsevier B.V., 2007, 91--108. The present version reports solutions of some problems, uses up-to-date notation, and update bibliography. Comments and further updates would be appreciated.