The perception of surface albedo (lightness) is one of the most basic aspects of visual awareness. It is well known that the apparent lightness of a target depends on the context in which it is embedded, but there is extensive debate about the computations and representations underlying perceived lightness. One view asserts that the visual system explicitly separates surface reflectance from the prevailing illumination and atmospheric conditions in which it is embedded, generating layered image representations. Some recent theory has challenged this view and asserted that the human visual system derives surface lightness without explicitly segmenting images into multiple layers. Here we present new lightness illusions--the largest reported to date--that unequivocally demonstrate the effect that layered image representations can have in lightness perception. We show that the computations that underlie the decomposition of luminance into multiple layers under conditions of transparency can induce dramatic lightness illusions, causing identical texture patches to appear either black or white. These results indicate that mechanisms involved in decomposing images into layered representations can play a decisive role in the perception of surface lightness.