The OECD's Programme for the International Assessment of Adult Competencies (PIAAC) represents a comprehensive international comparative assessment of the information processing skills of adults vital for the full participation in social and economic life in the 21st century. PIAAC is now in its second cycle and continues a series of international assessments of adult skills that began in the mid-1990s with the International Adult Literacy Survey (IALS). The Assessment Frameworks for Cycle 2 of PIAAC provide an essential background for understanding the skills assessed by the PIAAC assessment and for interpreting the results of the study. The Assessment Frameworks define and describe the skills assessed in the study -- literacy, numeracy and problem solving -- and outline the key features of the assessment of these skills. In addition, the relationship between Cycle 2 of PIAAC and previous assessments of these skills among the adult population is explained and an overview is provided of the changes that have occurred in the conceptualisation of these skills in the different international assessments of adult skills implemented over the last two decades.