When the right eye and the left eye view dissimilar scenes, the observer does not experience a stable superimposed percept of the images presented to the two eyes, but instead perceives an alternation between the images seen by each eye. A critical question confronting this robust and intriguing phenomenon of binocular rivalry is how the visual system selects the image to be perceived (dominant). The current main-stream literature emphasizes a bottom-up explanation in which the rivalry stimulus with the higher contour strength has the advantage, and becomes dominant in rivalry. Nevertheless, some workers in the past have favored an attention-selection explanation for binocular rivalry. We investigated the role of attention in binocular rivalry by employing novel psychophysical paradigms which capitalized on several established phenomena (e.g. the Cheshire Cat effect, attention cueing, pop-out effect). Our results revealed two major aspects of attention modulation in binocular rivalry. We found that a dominant image is less likely to be suppressed when voluntary attention is directed to it. This suggests the role of voluntary attention in retaining the dominant image in visual awareness. Second, a rivalry stimulus is more likely to become dominant if accompanied by a pop-out cue (in the same eye and proximity). Since a pop-out cue attracts involuntary attention to its location/eye, this result suggests that cue-mediated involuntary attention can promote the ability of a rivalry stimulus to reach visual awareness.