Oscillations in the 7-10 Hz and 40 Hz frequencies are characteristic of cerebral cortical circuits. Our laboratory began its study of the origins and possible computational significance of these patterns of activity a number of years ago by constructing biologically realistic network models of cerebellar cortical circuits (Wilson and Bower, 1991; 1992). These models suggested that cerebral cortical circuits naturally oscillate at these frequencies through a mechanism dependent on the interaction of time constants associated with both excitatory and inhibitory synaptic circuits. The dynamical behavior of the models was interpreted to suggest that cortical oscillations were responsible for coordinating the timing of computational cycles within these networks. The models also lead to the prediction that network level oscillations played an important role in coordinating the flow of synaptic information onto the dendrites of cortical pyramidal cells. In this workshop I will present the results of more recent single cell modeling efforts which support this view. I will conclude by presenting a general computational framework for understanding the role of oscillatory behavior in cerebral cortical function.