This paper describes the basic concepts of linking educational assessments. Although it discusses statistical machinery for interpreting evidence about students' achievements, this paper's principal message is that linking tests is not just a technical problem. Technical questions can not be asked or answered until questions about the nature of learning and achievement and about the purposes and consequences of assessment are addressed. Some fundamental ideas about educational assessment and test theory (chains of inferences and roles of judgment) are considered. The following approaches to linking assessments are described: (1) equating in physical measurement and educational assessment; (2) calibration in physical measurement and educational assessment; (3) projection in physical measurement and educational assessment; and (4) statistical moderation and social moderation. Implications for a system of monitoring progress toward educational standards are discussed. The following obtainable goals are highlighted: (1) comparing levels of performance across clusters directly in terms of common indicators of performance on a selected sample of consensually defined tasks administered under standard conditions; (2) estimating levels of performance of groups or individuals within clusters at the levels of accuracy demanded by purposes within clusters; (3) comparing levels of performance across clusters in terms of performance ratings on customized assessments in terms of a consensually defined, more abstract description of developing competence; and (4) making projections about how students from one cluster might have performed on the assessment of another cluster. Seven tables, 14 figures, and 41 references are included. (RLC)