This chapter describes aspects of the influence and application of the Danish Mathematical Competencies (KOM) Framework on the OECD’s Programme for International Student Assessment (PISA) assessment of mathematical literacy and its reporting. A KOM-inspired ‘mathematical competencies perspective’ has informed the development of PISA mathematics survey instruments. This exploration aims to show how such a perspective has helped researchers to better understand the cognitive demand of mathematics tasks in an assessment context and has enhanced their ability to devise assessment tasks that better reflect PISA’s mathematical literacy goals. The exploration reflects on both the traditional paper-based and the new digital assessment tasks employed in PISA in 2012. An overriding goal of the exploration is to build the case for making use of a competencies perspective on mathematics education and its assessment in the twenty-first century where digital tools have become commonplace. The links between KOM and PISA are introduced, followed by a summary of research that explored the relation between the difficulty of PISA assessment questions and the activation of different mathematical competencies. The next section describes and reflects on how that research, and its consequent version of the KOM-inspired PISA mathematical competencies, were used in the process of developing the assessment instruments for the PISA 2012 assessment. Next, the competencies are used in a new analysis that looks to see if there are differences between the paper-based and the digital components of mathematics in PISA 2012. Finally, lessons learned from the use of the KOM-like set of competencies are summarised.