In this work we report on theoretical calculations of methanol adsorption and dissociation on the stoichiometric and defective TiO2(110) surface. The periodic implementation of density functional theory (DFT) with plane waves and pseudopotentials was employed. A supercell made of 4 x 1 unit cells was used to represent the surface, which corresponds to methanol coverage of 0.25 ML. The defective surface was modeled by removing one bridging oxygen from the outermost layer. Several adsorption sites were explored through both static and molecular dynamics calculations. The most stable adsorption site on the defective surface is with the molecule directly adsorbed onto the vacancy, whereas adsorption on titania resembles the stoichiometric case. Our estimated adsorption energies are found to be in agreement with the features observed in previous experimental desorption data. One of the main aims of this study was to determine whether methanol could dissociate on the stoichiometric surface. From static calculations we find that both the molecular and the dissociated state are almost degenerate. In addition, molecular dynamics calculations show that the transition barrier between the two species is small. On the other hand, dissociation on defects is thermodynamically favorable by 0.5 eV. However, dynamic calculations show that in this case the conversion from the molecular to the dissociated state is not straightforward. Implications to these findings are discussed within the text.