This paper reviews the main features of the transport properties of single fractures. Particular attention is paid to fractures in geological materials which often display a roughness covering a broad range of length scales. Because of the small distance separating the fracture walls, the surface roughness is a key parameter influencing the structure of the void space. Studies devoted to the characterization of the surface roughness are presented as well as works aimed at characterizing the void space geometry. The correlation of the free space is found to be a crucial function of the failure mechanism (brittle, quasi brittle, plastic, etc) and also of possible shear displacements during the failure. The influence of the surface roughness on the mechanical behaviour of fractures under a normal load and a shear stress is also described. Finally, experimental, numerical and theoretical works devoted to the study of the influence of the fracture void geometry on the permeability and on the hydrodynamic dispersion of a dissolved species are discussed.