The new Knowledge Society requires new competences, which are known as 21st Century Competences. These competences are subdivided into competencies of higher-order thinking and competences in information and communication technologies. The aim of this article is to determine the dimensional structure of 21st century competences, together with key personal factors in this regard. This is a correlational study, based on a survey design, whose sample is constituted by students of the degrees of Pedagogy and Social Education at University of Valencia, selected by a non-probabilistic and accidental sampling, collecting the information by means of two questionnaires. The results point out that the competences for the 21st century are composed of two subsets, the competences of higher-order thinking and the ICT competences, which form a whole. In addition, it has been found that personal factors have a significant impact on this structure. It is suggested that education policies should address both aspects, in order to train citizens included in the Knowledge Society.