Abstract:Theoretical model hasbeen one of the most significant issues in the network sciences.First of all, three milestones in this area are reviewed asbreakthroughs in theoretical models, and progress in weightedevolution network model is presented. In order to describe thedeterminist and randomness of the harmony and unity of the realworld and to mirror overall property of the real-world networks,the unified hybrid network theoretical frame, which formed theso-called hybrid network theoretical model trilogy, are reviewedand summarized in the main part of this article: the first of thetrilogy is a harmonious unification hybrid preferential model(HUHPM), the second the large unification hybrid network model(LUHNM) and the third the large unified hybrid variable growthmodel (LUHVGM). Main features and topological properties of thehybrid network trilogy are then summarized, and diversity andcomplexity of the complex networks are revealed as well as theircomplicated transition relationship. Possible applications ofthese theories to actual networks are finally mentioned.