This article presents a review of the colloidal and liquid-crystalline properties of vanadium pentoxide suspensions from a physicist's perspective. The processes occurring during the synthesis of these suspensions are first discussed. Then, the liquid-crystalline properties of V2O5 sols and gels are described. These nematic phases are easily aligned by weak magnetic fields or by alternative electric fields. The delicate interplay between repulsive hardcore and electrostatic interactions and van der Waals attractions defines the (concentration, ionic strength) phase diagram that includes an isotropic phase, a uniaxial nematic phase, a biaxial nematic gel state and a flocculated state. Deuterium NMR spectroscopy of D2O molecules gives information on the rotational dynamics of the nematic phase. Finally, various applications of these colloidal suspensions in the fields of hybrid organic/inorganic materials, mesoporous solids, and of the structures of biomolecules, are reviewed.