Visual context often plays a crucial role in visual processing. In the domain of visual motion processing, the response to a stimulus presented to a neuron's classical receptive field can be modulated by presenting stimuli to its surround. The nature of these center-surround interactions is often inhibitory; the neural response decreases when the same direction of motion is presented to center and surround. Here we use binocular rivalry as a tool to study center-surround interactions. We show that magnitude of surround suppression varies as a function of luminance contrast and surround width. Increasing the size of surround motion increased surround suppression at high contrast. Furthermore, large, high-contrast surrounds facilitated opposite-direction motion in the center. For stimuli presented at low contrast, surround suppression peaked at a smaller surround width. In addition, we provide evidence that surround inhibition occurs at multiple levels of visual processing: Surround inhibition in motion processing is likely to originate from both monocular and binocular processing stages.