It is argued that it is fruitful to examine cognitive development from a domain-specific, conceptual change (CC) point of view, but that both domain-specific and domain-general approaches are necessary in order to understand how cognitive development happens. The article starts with a description of the framework theory approach to CC and an explanation of how this approach can account for students' difficulties in learning counter-intuitive science and math concepts. Framework theories do not seem to go away but continue to exist and interfere with access to scientific and mathematical concepts even in skilled adults. It is further argued that domain-general executive function abilities are involved in CC processes that require the inhibition of intuitive concepts embedded in framework theories. The article concludes with the suggestion that cognitive development may be seen from the lenses of dual-process theories and that the interactions between domain-specific CCs and domain-general processes may be responsible overtime for the development of new conceptual structures and new types of processing.