I will present a model cat visual thalamocortical system (Hill and Tononi, 2005) containing ~65,000 integrate-and-fire neurons and 6 million connections capable of producing rich spontaneous activity as well as orientation-selective responses to visual stimuli during wakefulness. The model encompasses two visual areas divided into three layers (supragranular, infragranular and layer IV) with the associated thalamic and reticular thalamic nuclei. Model neurons (both excitatory and inhibitory) are highly interconnected with patterned thalamocortical, corticothalamic, and intra- and interareal corticocortical connections. The model also incorporates experimentally observed intrinsic currents that are thought to affect sleep rhythms. The model exhibits a waking mode, characterized by highly variable spontaneous activity throughout the cortex as well as orientation selective responses to visual stimuli. Evoked visual activity displayed gamma frequency thalamocortical synchronization. In the sleep mode, the model displays spontaneously occurring slow oscillations that resemble those observed in vivo and in vitro. I will also present results from studies in which this model has been used to explore homeostatic processes and plasticity - including the synaptic homeostasis hypothesis of sleep.