Abstract: This paper is concerned with Edgeworth expansions for a general class of statistics under very weak conditions. Our approach unifies the treatment for both standardized and studentized statistics that have been traditionally studied separately under usually different conditions. These results are then applied to several special classes of well-known statistics: -statistics, -statistics, and functions of sample means. Special attention is paid to the studentized statistics. We establish Edgeworth expansions under very weak or minimal moment conditions.