A multiphysics model for liquid-feed Direct Methanol Fuel Cells is presented. The model accounts for two-dimensional (2D) across-the-channel anisotropic mass and charge transport in the anode and cathode Gas Diffusion Layers (GDLs), including the effect of GDL assembly compression and electrical contact resistances at the Bipolar Plate (BPP) and membrane interfaces. A one-dimensional (1D) across-the-membrane model is used to describe local species diffusion through the microporous layers, methanol/water crossover, proton transport, and electrochemical reactions, thereby coupling both GDL sub-models. The 2D/1D model is extended to the third dimension and supplemented with 1D descriptions of the flow channels to yield a 3D/1D + 1D model that is successfully validated. A parametric study is then conducted on the 2D/1D model to examine the effect of operating conditions on cell performance. The results show that an optimum methanol concentration exists that maximizes power output due to the trade-off between anode polarization and cathode mixed overpotential. For fixed methanol concentration, cell performance is largely affected by the oxygen supply rate, cell temperature, and liquid gas saturation levels. There is also an optimal GDL compression due to the trade-off between ohmic and concentration losses, which strongly depends on BPP material and, more weakly, on the actual operating conditions. (C) 2016 Elsevier Ltd. All rights reserved.