This article outlines the main assessment traditions in four countries -- England, France, Germany and the United States -- in order to explore the prospects for the integration of summative and formative functions of assessment during compulsory schooling. In England, teachers' judgments do feed into national assessments, at 7, 11, 14 and 16, but concerns for reliability and accountability mean that such judgments are made in a way that has little impact on learning. In France, teachers have no involvement in the formal assessment of students, and, possibly as a result, have been free to concentrate on the use of assessment to serve learning. In Germany, faith in the education system has been considerably undermined by recent unfavourable international comparisons, although faith in the ability of tests both to measure learning accurately and to allocate students to different educational pathways appears to be unshaken. In the United States, multiple demands for accountability at different levels of the system have resulted in multiple assessment systems, but these tend to be focused on measuring the amount of learning that has taken place, providing little insight into how it might be improved. It is concluded that the effective integration of formative and summative functions of assessment will need to take different forms in different countries, and is likely to be extremely difficult.