Measuring achievement and skills is fundamental in educational research and practice. The usefulness and interpretation of different measures depend on the goals of the assessment, the underlying theoretical account and its methodological implications, and the quality of the assessment itself. Preceded by an introduction, the present chapter first discusses general conceptual and terminological issues and challenges with a focus on the structure of cognitive and academic abilities and the implications for the measurement of skills and achievement. In the next section, we present three different views on competencies as major achievements due to learning and instruction (competencies conceptualized from a functional literacy perspective; modelled with reference to cognitive structures and processes and with reference to subcomponents or qualifications) and draw some general conclusions with respect to the assessment and interpretation of these measures. In the last section, we describe standards and modes of assessment, thereby differentiating between purposes of assessment, standards of test construction and modes of assessment. Implications for (sociological) research are indicated.