The paper examines difficulties in identifying and serving gifted minority students, especially Blacks. Approaches that have been tried and found unsuccessful (such as using preparatory programs to try to bring students' IQ scores to the acceptance level for program admission) are reviewed. Research is described on traits exhibited by gifted minority students, such as high nonverbal fluency and orginality and imagery-rich language. Examples of gifted minority students are cited to illustrate difficulties in identification. Difficulties inherent in testing minority students are analyzed, and ways of using traditional instruments as part of multiple criteria are suggested. (CL)