In this introductory paper we briefly sketch how, against the background of important changes in psychology from the late 1950s onward, research in (psychology of) mathematics education has been emerging as a field in its own right. While in the beginning psychology played the role of the major contributory discipline for this new field, the supremacy of psychology was increasingly challenged. Furthermore, the impact of cognitive psychology as the leading psychological orientation decreased and other psychological orientations, such as socio-constructivism, situated cognition, and Vygotsky's theory became more influential. During the past few years, there seems to be a renewed interest among researchers of mathematics education for cognitive psychological theories, such as Baddeley's model of working memory, Sweller's cognitive load theory, Siegler's model of strategy choice and change, various dual process theories, or Dehaene's triple code model of numerical cognition. In the present special issue, four papers describe, illustrate and discuss the potential relevance for four of these cognitive theories for understanding and improving mathematics learning and teaching.