A theory of illusory transparency and lightness is described for monocular and binocular images containing X-, T- and I-contour junctions. This theory asserts that the geometric and luminance relationships of contour junctions induce illusory transparency and lightness percepts by causing a phenomenal scission of a homogenous luminance into multiple contributions. Specifically, it is argued that a discontinuous change in contrast along aligned contours that preserve contrast polarity induces a scission of the lower contrast region into a near-transparent surface or an illumination change, and a more distant surface that continues behind behind this near layer. This scission is assumed to cause changes in perceived lightness and/or surface opacity. Discontinuous changes in contrast along contours also are assumed to induce end-cut illusory contours that run roughly perpendicular to the inducing orientation of the contour, both monocularly and binocularly. Binocular illusory contours are shown to be caused by the presence of unmatchable contour terminators. It is argued that the presented theory can provide a unified account of a variety of monocular and binocular illusions that induce uniform transformations in perceived lightness, including neon-color spreading, the Munker-White illusion, Benary's illusion, and illusory monocular and binocular transparency.