We investigated the spatial organization of surround suppression in primate primary visual cortex (V1). We utilized drifting stimuli, configured to extend either from within the classical receptive field (CRF) to surrounding visual space, or from surrounding visual space into the CRF or subdivided to generate direction contrast, to make a detailed examination of the strength, spatial organization, direction dependence, mechanisms, and laminar distribution of surround suppression. Most cells (99/105, 94%) through all cortical layers, exhibited suppression (mean reduction 67%) to uniform stimuli exceeding the CRF, and 43% exhibited a more than 70% reduction. Testing with an annulus revealed two different patterns of surround influence. Some cells (37% of cells), classical surround suppression (CSS) cells exhibited responses to an annulus encroaching on the CRF that were less than the plateau in the spatial summation curve. The majority (63%), center-gated surround suppression (CGSS) cells, showed responses to annuli that equaled or exceeded the plateau in the spatial summation curve. Analysis suggested the CSS mechanism was implemented in all cells while the CGSS mechanism was implemented in varying strength across the sample with the extreme reflected in cells that gave larger responses to annuli than to a center stimulus. Reversing the direction of motion of the portion of the stimulus surrounding the CRF revealed four different patterns of effect: no reduction in the degree of suppression (22% of cells), a reduction in surround suppression (41%), a facilitation of the response above the level to the inner stimulus alone (37%), and a facilitation of the response above that to the inner stimulus alone that also exceeded the values associated with an optimal inner stimulus. The facilitatory effects were only seen for reverse direction interfaces between the central and surrounding stimulus at diameters equal to or more than the CRF size. The zones driving the suppressive influences and the direction contrast facilitation were often spatially heterogeneous and for a number of cells bore strong comparison with the class of behavior reported for surround mechanisms in MT. This suggests a potential role, for example, in extracting information about motion contrast in the representation of the three dimensional structure of moving objects.