The potential energy surfaces for the insertion reactions of methylene and fluorinated methylenes into the H-2, HF, and F-2 molecules were studied by density functional, many body perturbation, and coupled-cluster theories. These methods predict the barrier for the CF2 insertion into the hydrogen molecule to be about 33 kcal/mol, that is, significantly lower than previous estimates. A new transition state was found in this system for the reaction path which leads to CHF + HF. However the transition state for this metathesis channel is about 25 kcal/mol higher than that of the insertion channel. For the fluoromethylene insertion into H-2 the predicted activation energy is about 8 kcal/mol. The CH2 insertion into F-2 proceeds without a barrier. The peculiarity of the insertion reactions between carbenes and HF involves formation of a hydrogen-bonded complex. The CH2 ... HF complex is bound by about 10 kcal/mol relative to CH2 + HF. Coupled-cluster methods predict a small (ca. 3 kcal/mol) barrier for transformation of this complex into CH3F. However, this barrier lies 7 kcal/mol below reactants CH2 + HF. In the case of the CHF insertion into HF the analogous barrier is higher and lies ca. 2 kcal/mol above reactants.