Topological relationship is one of the most important theoretical topics related to GIS modeling

and it plays a key role in many geo-technical fields such as spatial data modeling

spatial query

spatial analysis

spatial reasoning

and cartographic generalization. To motivate further research and applications of the theory

this paper reviews the formalisms and formal models of topological relations. First

the approaches that describe topological relations under certainty are briefly examined. Then the developing progress toward topological relations with uncertainties is explored in terms of research methodologies

including broad boundary approach

fuzzy set approach

random set approach

and rough set approach. Moreover

some applications of the theory in spatial query

spatial analysis and spatial reasoning

are basically introduced. Finally

several issues are highlighted for future investigations.