Catalytic residues play a significant role in enzyme functions. With the recent accumulation of experimentally determined enzyme 3D structures and network theory on protein structures, the prediction of catalytic residues by amino acid network (AAN, where nodes are residues and links are residue interactions) has gained much interest. Computational methods of identifying catalytic residues are traditionally divided into two groups: sequence-based and structure-based methods. Two new structure- based methods are proposed in current advances: AAN and Elastic Network Model (ENM) of enzyme structures. By concentrating on AAN-based approach, we herein summarized network properties for predictions of catalytic residues. AAN attributes were showed responsible for performance improvement, and therefore the combination of AAN with previous sequence and structural information will be a promising direction for further improvement. Advantages and limitations of AAN-based methods, future perspectives on the application of AAN to the study of protein structure-function relationships are discussed.