An attempt is made to clarify the aims of critical training in academic subjects at the higher education level. Additionally, common motifs of thought in the extensive material of cognitive criticism are considered, and the material itself is synthesized. Attention is also directed to the criteria of essentiality and implications for teaching. Two important dimensions related to critical training are attitudes and methods. Studies have examined the concepts of independence, tolerance, problem awareness, and intellectual maturity. These concepts are viewed as entailing both psychological and methodological domains. The study of critical practice has been extensive in addressing material concerning historical source criticism, legal technique, the psychology of testimony, the sociology of knowledge, and other areas. In this approach emphasis is placed on insights and methodological ideas whose significance transcends subject boundaries. Certain supporting inquiries have been undertaken concerning medicine, political science, and history. The analysis of historical science has been almost entirely concerned with questions relating to selection and criteria of essentiality. One important consideration in all selection is the attempt to bring the cognitive material under control. It is concluded that a focal point in the analyses has been the link between education and research and the importance of critical training. It is suggested that the choice between the essential and the nonessential is important both to teacher planning and student learning. (SW)