Critical thinking (CT) is considered a key skill for success in the 21st century. Worldwide educational policies advocate the promotion of CT, and researchers across different fields have been involved in a wide debate on its definition, without reaching an agreement. Currently, research has not adequately addressed CT assessment, nor the way in which it should be taught. In the present work, an overview of the topic is provided, as well as an evaluation of the practices, in order to provide researchers or practitioners (particularly those involved in primary school education) a reference for the development of further theories and methods about CT in education. We consider CT from the perspective of philosophy, cognitive psychology, and education sciences, and in addition, we propose the inclusion of a fourth, which could be referred as socio-cultural pedagogic perspective, due to its important implications in teaching and assessment practices.