One of the major challenges in neuroscience is to understand the biophysical mechanisms and algorithms underlying neural computation. In my research group, we use mathematical models, analysis, and computer simulations to examine the dynamics of neurons and neuronal networks. Our goal is to understand the mechanisms underlying alterations in neuron or network behavior due to trauma, rehabilitation, learning or development. My research group also contributes to an international effort to create standards for describing models in neuroscience. NeuroML provides a common format for neuroanatomical data, for the biophysical properties of membranes, and for network connectivity. These standards are used by down-stream software applications to aid model exchange and simulator interoperability.