The lightness of a test patch completely surrounded by an inducing field can be predicted by variants of Wallach's ratio rule. When a patch is surrounded by two or more regions with different luminances, a plausible extension of the ratio rule would predict that the effect of the surrounding regions should correlate with the length of the border they share with the test patch. However, as shown by the Wertheimer-Benary and White effects, lightness of such patches can depart appreciably from these predictions. It is argued that a fruitful approach toward the explanation of such effects is based on the analysis of junctions (such as T-junctions and X-junctions) between regions. Several new displays and variations of old displays involving such junctions are used to illustrate this approach. An alternative analysis of a lightness effect introduced by Adelson is provided, and the role of depth effects in achromatic perception is discussed. A number of limitations of the approach and possible ways to overcome them are noted.