We will discuss our attempts to study neural correlates of the perceptual alternations experienced upon viewing of ambiguous figures, and relate them to new psychophysical evidence offering a new twist in the eye-versus-percept debate. Our studies over the last decade indicated that perception-responsive cells are concentrated in cortical areas near the top of the processing hierarchy, but that they can be found all along the visual pathway. Similarly, psychophysics has shown that both, monocular as well as binocular, percept based neural representations contribute to perceptual dominance. Our new psychophysical evidence suggests a time-dependence of eye and percept contributions in binocular rivalry: initially a given monocular channel has greater influence on dominance, regardless of the percept. Over time, this reverses, with percept-related (ie eye-independent) processes increasingly `urging' for a perceptual switch. We suggest this may reflect a single process, where monocular as well as binocular neural stages affect each other in a feedback-loop that evolves over time. Understanding rivalry thus calls for the study of networks rather than single neurons.