In recent years assessment has attracted increased attention from the international mathematics education community including this Korean community also. There could be numerous reasons for this phenomena. During the last couple of decades the field of mathematics education has developed considerably in the area of goals, theories, and practices. Whereas these developments have not been matched by parallel development in assessment. Now the functions, roles, and effects of assessment in mathematics education should no longer be neglected, rather they should become objects of investigation and examination in the study of mathematics education. The purpose of this study is to explore selected international cases of assessment in mathematics education mainly depended on two studies resulting from ICMI Study Conference on Assessment in Mathematics Education and Its Effects; and then to draw out their suggestions needed for our study of assessments in mathematics education.