We discuss attempts to model aspects of human visual selection in a biologically plausible neural network – the spiking Search over Time and Space model (sSoTS). We show how, by incorporating physiologically realistic parameters into the model, aspects of human search over time as well as space can be captured. These parameters are also useful for simulating neuropsychological deficits in selection found in patients with lesions to posterior parietal cortex. Finally, we show how the model can be used to help decompose neural networks revealed by fMRI to be involved in spatial selection over time, providing a model-based analysis linking neuroanatomy to cognitive function. We discuss the utility of developing biologically plausible networks for high-as well as well as low-level cognitive operations.