Fractal geometry, in which infinite numbers of fractional dimensions are permitted in contradistinction to the three integer dimensions in Euclidean geometry, has been applied to the study of surface roughness. A tentative conclusion is that fractal geometry offers yet another vehicle for the physical chemist to meet the mechanical engineer on solving problems in the boundary lubrication regime of tribology. Of course, fractals have been applied to the study of turbulence which is within the fluid film lubrication regime. Other potential applications might include all processes in tribology which are stochastic in nature.Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Baltimore, Maryland, October 16–19, 1988