The concepts and powerful mathematical tools of Dynamical Systems Theory (DST) yield illuminating methods of studying cognitive processes, and are even claimed by some to enable us to bridge the notorious explanatory gap separating mind and matter. This article includes an analysis of some of the conceptual and empirical progress Dynamical Systems Theory is claimed to accomodate. While sympathetic to the dynamicist program in principle, this article will attempt to formulate a series of problems the proponents of the approach in (...) question will need to face if they wish to prolong their optimism. The main points to be addressed involve the reductive tendencies inherent in Dynamical Systems Theory, its somewhat muddled position relative to connectionism, the metaphorical nature DST-C exhibits which hinders its explanatory potential, and DST-C's problematic account of causality. Brief discussions of the mathematical and philosophical backgrounds of DST, seminal experimental work and possible adaptations of the theory or alternative suggestions (dynamicist connectionism, neurophenomenology, R&D theory) are included. (shrink)