How do the neural networks of the human brain generate the processes on which higher cognition is based? This is the long-standing challenge of a neural theory of higher cognition. Because cognitive competences emerge in evolution and development from the sensory-motor domain, a neural process account for higher cognition must be grounded in perception and action. How may the hallmarks of higher cognition, productivity, systematicity, and compositionality, emerge from such a bottom-up approach? The review paper just published in Cognitive Neurodynamics argues that the dynamic instabilities that are central to Dynamic Field Theory enable the autonomous generation of sequences of mental states. Through coordinate transforms implemented in neural gain fields and the flexible binding of localist neural representations through a shared index dimension, these sequences may exhibit productivity, systematicity, and compositionality. The ideas are illustrated in a neural dynamic architecture that represents and perceptually grounds nested relational and action phrases such as "the ball moves to the small tree that is to the left of the lake and and behind the large tree".