This monograph has grown out of a series of discussions and a six-month period of reading and reflecting on the literature which were initiated by Fritz Mosher's suggestions to the National Assessment of Educational Progress (NAEP) to examine the "standards" question. Conversations with Mosher himself and the staff of NAEP have been most influential. The Analysis Advisory Committee of NAEP, under Fred Mosteller's chairmanship, proved a rigorous testing ground for many of the ideas. Here, the author (a) examines the ordinary usage of the words "standards" and "criteria" in the measurement literature; (b) traces the evolution of the notion of performance standards in the criterion-referenced testing movement; (c) analyzes and critiques six methods of setting performance standards on criterion-referenced tests; and (d) reflects briefly on the political forces which have become focused on the standards issue. (Contains 7 figures, 2 tables and 7 footnotes.)