Three theories currently compete to explain the conceptual deficits that result from brain damage: sensory-functional theory, domain-specific theory, and conceptual structure theory. We argue that all three theories capture important aspects of conceptual deficits, and offer different insights into their origins. Conceptual topography theory (CTT) integrates these insights, beginning with A. R. Damasio's (1989) convergence zone theory and elaborating it with the similarity-in-topography (SIT) principle. According to CTT, feature maps in sensory-motor systems represent the features of a category's exemplars. A hierarchical system of convergence zones then conjoins these features to form both property and category representations. According to the SIT principle, the proximity of two conjunctive neurons in a convergence zone increases with the similarity of the features they conjoin. As a result, conjunctive neurons become topographically organised into local regions that represent properties and categories. Depending on the level and location of a lesion in this system, a wide variety of deficits is possible. Consistent with the literature, these deficits range from the loss of a single category to the loss of multiple categories that share sensory-motor properties.