The paper reviews the literature of the last 25 years to determine the accepted definitions of giftedness, underachievement, and gifted underachiever. The evolution of the concepts of giftedness and underachievement is recounted and various definitions are compared. The paper describes an attempt made to locate, by further review, useful instruments for the identification of gifted underachievers. Five objective instruments from the "Alphabetical Listing of Instruments" in the "National Report on Identification" are analyzed for their pertinent use; and J. Whitmore's "Checklist to Identify Gifted Underachievers" is included as useful in the identification of gifted underachievers by behavioral observation. It is concluded that researchers, in general, have been relatively non-productive in studying the identification of the gifted underachiever; consequently program planners are limited in the scope of their efforts. (Author/CL)