It is commonly assumed that the orientation-selective surround field of neurons in primary visual cortex (V1) is due to interactions provided solely by intrinsic long-range horizontal connections. We review evidence for and against this proposition and conclude that horizontal connections are too slow and cover too little visual field to subserve all the functions of suppressive surrounds of V1 neurons in the macaque monkey. We show that the extent of visual space covered by horizontal connections corresponds to the region of low contrast summation of the receptive field center mechanism. This region encompasses the classically defined receptive field center and the proximal surround. Beyond this region, feedback connections are the most likely substrate for surround suppression. We present evidence that inactivation of higher order areas leads to a major decrease in the strength of the suppressive surround of neurons in lower order areas, supporting the hypothesis that feedback connections play a major role in center-surround interactions.