This issue of "ZDM Mathematics Education" focuses on the formative assessment of young children's mathematical thinking, with an emphasis on computer-based approaches drawing upon on cognitive and educational research. The authors discuss several different assessment methods, including clinical interviewing, observation, and testing, that are appropriate for children from about 3-8 years of age, and that can provide information useful for the improvement of teaching. This paper begins with a discussion of principles underlying this work and then introduces the paper topics and authors. The paper concludes by projecting a future in which professional development provides a sound basis for formative assessment; in which formative assessment is central to education; and in which the need for standard achievement tests is largely eliminated.