Complex network systems widely exist in nature and human society, hence its research carries broad significance. How do we characterize and differentiate amongst a crystal lattice, the Internet and a food web? How do they evolve? Is there some kind of invisible organizing principle, hiding behind all these networks? In recent years our view of network systems has been greatly changed due to research supported by powerful computational facilities. Focussing on new concepts such as the small－world, clustering and scale－free systems, we review the progress in this field.