In this paper we have investigated the hydrogen abstraction reactions by methyl radical from fluoro-, chloro-, and bromomethanes using ab-initio (HF and MP2) and DFT-based methods. The DFT computations have been performed using different functionals, including nonlocal corrections in all cases. At all levels of theory the computational results have shown the following : (i) the reaction proceeds in one step through a transition state which shows a collinear or nearly collinear arrangement of the three atoms involved in the process, (ii) the only relevant effect of dynamic correlation on the geometry of the transition states is increase their reactant-like character (see MP2 and DFT results), (iii) the inclusion of dynamic correlation for reactants and transition states is essential to obtain reasonable values of the computed activation energies, and (iv) the energy barriers computed with the DFT approach are strongly dependent on the type of functional which is used. The best values have been obtained with the hybrid functional B3LYP which provides activation energies which are in better agreement with the experiment than the MP2 values which are in all cases quite overestimated. The present study indicates that the DFT method based on the B3LYP functional is suitable for investigating extensively this class of reactions. A simple diabatic model is used to rationalize the trend of reactivity observed when more halogen atoms are added to the substrate or when the halogen varies from fluorine to chlorine and bromine.