Book excerpt: It has only recently been acknowledged to what large extent the internal dynamics of neural networks could play a role in their function. In this respect, synaptic "noise" -- that is, the influence of the cortical network on single neurons exerted through the massive recurrent circuity that is the hallmark of neocortex -- has recently been shown to have a profound effect on neuronal integrative properties, changing the responses of single neurons across brain states, sometimes within the matter of a few seconds. These internally generated activity states, shaped by and continually shaping the plastic synaptic recurrent connections, then combine with the external inputs to produce a rich repertoire of responses to sensory stimuli in primary cortical regions. In this thesis, we have focused on the {\it spatial} aspect of these internal dynamics, specifically the spatial structure of cortical oscillations, spontaneous and stimulus-evoked. Along the way, we have made an extensive review of the literature concerning propagating waves in thalamus and cortex, and studied network models to investigate how waves depend on network state. We have also introduced new tools for the characterization of spatiotemporal activity patterns in noisy multichannel data. The culmination of this work is a demonstration, using voltage-sensitive dye imaging data taken from the awake monkey, that the population response to a small visual stimulus propagates like a wave across a large extent of primary visual cortex during the awake state, a result contradicting a range of previous studies which seemed to suggest that propagating waves disappear in this case. Moving forward, we have begun to investigate the spatiotemporal structure of local field potential and spiking activity in multielectrode recordings taken from the human and monkey in various states of arousal, to address questions prompted by our initial voltage-sensitive dye imaging study in the monkey. In parallel, we have initiated an analysis of the extent to which neural connectivity can be characterized by the "small-world" effect, the main result of which is that neural graphs may in fact reside outside the small-world regime. The results from these PhD studies thus span the spectrum of scales in neuroscience, from macroscopic activity patterns to microscopic connectivity profiles. It is my sincere hope to expound in these pages a unified theme for these results, and a foundation for further work in neuroscience -- a search for structure within the internal architecture of the system under study.