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The matrix expression, topological index and atomic attribute of molecular topological structure are reviewed. Nine ma- trices, twenty-six kinds of indices and eight methods dealing with weighted molecular graphs are summed up in three tables. Some shortcomings of the topological indices are discussed as: (1) the physical-chemical meaning of topological index is not explicit; (2) it is difficult to interpret the QSAR and QSPR models derived from the topological indices; and (3) topological index usually neglects the stereochemical information or the three-dimensional structure of the molecule. Three directions of topological index are focused on: (1) description of local information; (2) studies on inter-correlation of topological index; and (3) variable index.