To meet the demands of survival, the central nervous system has to simultaneously encode the external world and internal states in the spiking activity of neurons. Populations of neurons are connected by non-random synaptic wiring, shaped by previous experience, and in turn give rise to variable yet correlated spiking activity. This works attempts to relate the structure of spiking activity to its underlying, interconnected substrate on the one hand, and to the external variables they presumably encode on the other. To do so, statistical dependencies in the activity of neurons are summarized as functional networks (FNs), where neurons are nodes and the statistical regularities between them are edges. In this dissertation, FNs are utilized in encoding, decoding and both generative and discriminative models to gain insights into the circuit level representation of visual stimuli.As networks, FNs can be readily compared to anatomical and synaptic connectivity in neural network model. This comparison reveals that the structure of statistical dependencies depends on the timescale at which they are computed, and that neural activity has a more clustered structure than the synaptic wiring used in the model. In mouse primary visual cortex, this increased clustering is found to be characteristic of neurons that do not have a clear stimulus preference (i.e. untuned neurons). Moreover, regardless of single cell selectivity, the correlations between neurons are stimulus-specific and hence informative of the visual stimulus. Subsequently, a sparse subset of stimulus-specific pairwise interactions is identified. These correlations reliably manifest as pairs of coordinated spikes on a time-point by time-point basis, building up spatio-temporal sequences. When only these spikes are considered, single neurons still display high trial-to-trial variability. Nonetheless, these spikes have enhanced readability by hypothetical downstream elements.