The different methods for enhancing the catalytic activity of transition metal complexes in hydrocarbon (particularly, alkylarene) oxidations with dioxygen are briefly discussed. The role played by H-bonds in mechanisms of homogeneous catalysis is also analysed. Furthermore, the authors propose a strategy of controlling the catalytic activity of Fe(II,III)(acac)nL2 complexes (L2 = R4NBr or 18C6) by adding H2O to small concentrations. In addition, the activity of Ni, Fe, and Co catalysts in microsteps of chain initiation (O2 activation), and propagation (Cat + RO2?) in the radical chain process of ethylbenzene oxidation is assessed by original method offered by authors. New concepts of mechanism of chain process of hydrocarbon oxidations with dioxygen, catalysed with transition metal complexes, participation of catalysts in microsteps of complicated hydrocarbon oxidation, activity M-O2 (M = Co, Ni, Fe) complexes in different oxidation reactions are briefly stated, and the self-assembled (self-organised) systems mediated by transition metals are briefly considered in connection with increasing research interest in chemical transformations with use of these systems.