LuFe2O4 belongs to the rare-earth ferrite family RFe2O4 (R=Dy to Lu, Y), whose structure can be described as a stacking along c of [LuO2]∞ and [Fe2O4]∞ compact layers. This compound is attracting a lot of attention nowadays because of its multiferroic properties, linked to an antiferromagnetic spin ordering below Tn=250K and a ferroelectric state, based on a polar charge ordering of Fe2+ and Fe3+ species on a triangular lattice. In this work, two samples have been thoroughly investigated, combining synchrotron X-ray, neutron and electron diffraction techniques with magnetization, transport and dielectric constant measurements, as well as Mossbauer spectroscopy. Two main points have been evidenced: a slight monoclinic distortion of the room ...