The focus of this chapter is on the notion of mathematical competence and its varying role in the PISA mathematics frameworks and reports of PISA results throughout the first five survey administrations, in which mathematical literacy is a key concept. The chapter presents the genesis and development of the competency notion in Denmark, especially in the so-called KOM project, with a view to similar or related notions developed in different environments and contexts, and provides a detailed description of the eight competencies identified in the KOM project. Also the relationship between the mathematical competencies and the fundamental mathematical capabilities of the PISA 2012 Framework is outlined and discussed.