Line drawing interpretation has been investigated both in engineering and psychology. In engineering, it has been investigated under the condition that the line drawing represents the contour figure of a three-dimensional object. In psychology, there are many kinds of research on line drawing interpretation, from word perception to subjective contours. This paper first reviews what kinds of problems have been focused in both fields and what is left undone. This paper next shows how a cognitive science approarch can solve one of the unsolved problems, that is, the interpretation of overlapping figures. If there are no constraints, an infinite number of possible interpretations exist for overlapping figures. Humans, however, instinctively create a small number of natural interpretations. In order to obtain these interpretations, seven kinds of constraints were introduced. Some of them are technical, in the sense that they are introduced to reduce the number of possible interpretations. Others are psychological in the sense that they are obtained from human behavior on line drawing perception.