There are five sections in this survey paper. In section 1, we indicate why multiplier problems are of some interest. In section 2, we discuss the phenomenon that two distinct spaces of functions can have the same multipliers and relate this to a type of reflexivity. In section 3, we give a concise summary of known results on multipliers ofHpand related spaces. In section 4, we consider the problem of effectively describing multipliers instead of simply characterizing multipliers abstractly. The fifth and final section closes with a list of open problems.