A central question in visual neuroscience is what circuits generate the responses of neurons in the primary visual cortex (V1). V1 neurons respond best to oriented stimuli of optimal size within their receptive field (RF) center. This size tuning is contrast dependent, i.e. a neuron's optimal stimulus size measured at high contrast (the high-contrast summation RF, or hsRF) is smaller than when measured using low-contrast stimuli (the low-contrast summation RF, or lsRF). Responses to stimuli in the RF center are usually suppressed by iso-oriented stimuli in the extra-classical RF surround. Iso-orientation surround suppression is fast and long range, extending well beyond the size of V1 cells' lsRF. Geniculocortical feedforward (FF), V1 lateral and extrastriate feedback (FB) connections to V1 could all contribute to generating the RF center and surround of V1 neurons. Studies on the spatio-temporal properties and functional organization of these connections can help disclose their specific contributions to the responses of V1 cells. These studies, reviewed in this chapter, have shown that FF afferents to V1 integrate signals within the hsRF of V1 cells; V1 lateral connections are commensurate with the size of the lsRF and may, thus, underlie contrast-dependent changes in spatial summation, and modulatory effects arising from the surround region closer to the RF center (the "near" surround). The spatial and temporal properties of lateral connections cannot account for the dimensions and onset latency of modulation arising from more distant regions of the surround (the "far" surround). Inter-areal FB connections to V1, instead, are commensurate with the full spatial range of center and surround responses, and show fast conduction velocity consistent with the short onset latency of modulation arising from the "far" surround. We review data showing that a subset of FB connections terminate in a patchy fashion in V1, and show modular and orientation specificity, consistent with their proposed role in orientation-specific center-surround interactions. We propose specific mechanisms by which each connection type contributes to the RF center and surround of V1 neurons, and implement these hypotheses into a recurrent network model. We show physiological data in support of the model's predictions, revealing that modulation from the "far" surround is not always suppressive, but can be facilitatory under specific stimulus conditions.