In educational contexts, assessments may be designed to target students, preservice teachers, or teachers, either as individuals or as representatives of a group, and for a multitude of purposes. One key aim of assessment in mathematics education is to provide evidence that can be used to make decisions about or improve mathematics education, which then raises questions about which aspects of mathematical competence should be assessed--as well as how and for what purpose. This review paper addresses three related themes: (1) issues related to the assessment process and to the development of assessments that can validly assess mathematical competence in all its complexity; (2) issues related to educational policy and policy-making based on assessment data, in particular the reciprocal relationship between assessment and policy; and (3) issues related to equity, such as gender issues or the achievement gap between majority and minority students. Awareness of the relation between assessment, teaching, and learning is shown throughout the paper. Strong relationships between the three focus areas are found, that impact assessment validity and call for further development of assessment practices in mathematics education.