Many models of cognitive processes describe behavior in terms of underlying latent variables, such as our beliefs about the state of the world. But how can such models be realized in neural circuits? In this talk, I will present the framework of "computation through dynamics" to describe how populations of neurons can represent and transform information with dynamical systems over low-dimensional manifolds. I will then present a method for designing recurrent neural network models that implement specific dynamics. Finally, I will use this technique to construct a network model capable of generalizable, flexible computations in a timing task. Overall, this talk will show how one can test assumptions about the geometry and dynamics of neural representations in cognitively interesting tasks.