In recent years, there has been a growing interest in Classification among various scholars connected with cultural and social anthropology. It can be said that Classification is a key concept as an explanatory principle and a methodological device for understanding other cultures. On the other hand, however, there is considerable discrepancy in the usage of that concept, resulting in disagreement and controversy between different schools. Ethnoscience (in U.S.A) and Symbolic Classification (in Europe), discussed in this paper, are two main schools that have had no contact with each another so far. Ethnoscience, including Ethnosemantics, New Ethnography and Cognitive Anthropology, etc., has concentrated on practical, everyday classification, and developed a formal analysis which was rigid and detailed. On the other hand, Symbolic Classification has, as its name suggests, emphasis on symbolic aspects of classification, and produced many penetrating analyses that were based on "thick description" (after C. Geertz). But, paradoxically speaking, it can be pointed out that "those that have been sociologically sophisticated have often been technically and empirically weak, and those that have been technically and linguistically rigorous have frequently been sociologically naive", as R. Ellen wrote. Certainly, each field has many unique problems, but some problems should be dealt with in common. The purpose of this paper is to examine some existing problems in each field, in the hope of working towards a general theory of Classification.