An overview of the PISA project is given in order to set a context for a consideration of the ways in which this large international assessment programme uses scientific measurement principles and techniques. The overview describes the goals of the project, its major organisational features (its participants, its procedures and organisational structure, its main implementation steps) and its major technical components (test design, test development, sampling, assessment operations, data scaling and analysis, and reporting). The ways in which measurement principles are used are interwoven with the discussion of the relevant technical components. The paper concludes with a detailed discussion of the construction of the described proficiency scales used to report outcomes for PISA mathematics.