In this chapter I look closely at the intentionality of consciousness from a naturalistic perspective. I begin with a consideration of Gurwitsch's suggestive ideas about the role of acts of consciousness in constituting both the objects and the subjects of consciousness. I turn next to a discussion of how these ideas relate to my own empirical approach to intentional relations seen from a developmental perspective. This is followed by a discussion of some recent ideas in philosophical cognitive science on the intentionality of consciousness, both with respect to the objects and the subjects of consciousness. I show that these recent trends tend to naturalize intentionality and consciousness in directions compatible with the descriptive aspects of Gurwitsch's constitutive phenomenology.