Various theoretical studies of σ-bond activation of organic molecules by transition metal complexes arereviewed. In the homolytic σ-bond activation, the d orbital energy level of the central metal is an importantfactor, as well known. At the same time, the electron-withdrawing substituent which stabilizes the sp3 orbitalaccelerates the homolytic σ-bond activation. In the heterolytic C-H σ-bond activation of RH by $MXL_n$, the XHbond formation is an important driving force, where $MRL_n$ and HX are formed as products. The heterolytic σ-bond activation is also understood in terms of the electrophilic attack of the metal center to the substrate.