This paper is meant to examine the problems and research that has been done in the area of identifying the students that may show extreme giftedness in one subject and perform low in another, those who may be overlooked due to cultural, linguistic or ethically diverse backgrounds and those students who may not score well on standardized tests; to include twice exceptional students.Identification and low representation of culturally, linguistically, and ethnically diverse (CLED) students have been a concern with researchers and educators in our country. Considering the changing demographics within schools and pressure from the government and funding issues, educators must examine "how to change identification procedures and services to adequately recognize and develop these students' talents" . Even though cultural diversity has become more prominent in in education, CLED students are more identified in the remedial classes and underrepresented in gifted and talented programs .National surveys show that only 10% of those students performing at their highest level are CLED students even though they represent 33% of the school population (Gallagher, 2002). The issues of identifying and assessing such students are highly important due to various reasons, but first of all because the absence of proper educational approach and environment hinder the development and future success of a great number of people, which undermines the very mission of education. Researching methods and approaching for identification and assessment of nontraditional gifted students will help to address this deficiency of our educational system.