The discovery of exceptionally high catalytic activities of small Au particles has initiated intense research activity to understand their origin. In spite of a large volume of work, the system is far from being fully understood. There are four major issues in Au-catalyzed CO oxidation that have not been resolved: (1) the importance of the nature of the support on catalyst activity; (2) the Au oxidation state necessary for high activity; (3) the sensitivity of the activity to the moisture level in the reaction feed; and (4) reasons for the high activity in small Au particle size and for the strong dependence on particle size and specific morphology. The current understanding of these issues based on available experimental evidence and computational investigations is discussed, as well as aspects that remain unresolved.