The development of green chemistry has attracted the chemists' attentions in recent years. Among them, Milstein and coworkers have discovered a new mode of metal-ligand cooperation in complexes, where an aromatization-dearomatization process of the pyridine or acridine-based PNP and PNN "pincer" ligands appears to be a key element. These complexes were reported to lead to unusual X-H (X=H, C, O, N, and B) activation reactions and to environmentally benign catalysis involving dehydrogenative coupling reactions and hydrogenation reactions, representing an important development in green chemistry. This review provides a summary of theoretical studies on the mechanisms of the reactions mediated by transition metal complexes with noninnocent pincer ligands synthesized by Milstein and coworkers. The aromatization-dearomatization process of the pyridine or acridine-based PNP and PNN "pincer" ligands were found to play important roles in some reactions, while other reactions do not involve the aromatization-dearomatization process. For some reactions, several research groups proposed different mechanisms to explain the same reaction. Thus, to compare these mechanisms, we recalculate their rate-determining steps by using the functionals that are calibrated to produce results close to those from coupled cluster calculations. Moreover, the understanding of the reaction mechanisms can help researchers to improve the current reactions and design new reactions.