In the literature on dynamical models in cognitive science, two issues have recently caused controversy. First, what is the relation between dynamical and mechanistic models? I will argue that dynamical models can be upgraded to be mechanistic as well, and that there are mechanistic and non-mechanistic dynamical models. Second, there is the issue of explanatory power. Since it is uncontested the mechanistic models can explain, I will focus on the non-mechanistic variety of dynamical models. It is often claimed by proponents of mechanistic explanations that such models do not really explain cognitive phenomena (the ‘mere description’ worry). I will argue against this view. Although I agree that the three arguments usually offered to vindicate the explanatory power of non-mechanistic dynamical models (predictive power, counterfactual support, and unification) are not enough, I consider a fourth argument, namely that such models provide understanding. The Voss strong anticipation model is used to illustrate this.