The application of the field of network science to the scientific disciplines of structural biology and biochemistry, have yielded important new insights into the nature and determinants of protein structures, function, dynamics and the folding process. Advancements in further understanding protein relationships through network science have also reshaped the way we view the connectivity of proteins in the protein universe. The canonical hierarchical classification can now be visualized for example, as a protein fold continuum. This review will survey several key advances in the expanding area of research being conducted to study protein structures and folding using network approaches.