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Biological neural systems are well known for their robust and power-efficient operation in highly noisy environments. We outline key modeling abstractions for the brain and focus on spiking neural network models. We discuss aspects of neuronal processing and computational issues related to modeling these processes. Although many of these algorithms can be efficiently realized in specialized hardware, we present a case study of simulation of the visual cortex using a GPU based simulation environment that is readily usable by neuroscientists and computer scientists and efficient enough to construct very large networks comparable to brain networks.