The nonstationary character of roughness is a widely recognized property of surface morphology and suggests modeling several solid surfaces by fractal geometry. In the field of contact mechanics, this demands novel investigations attempting to clarify the role of multiscale roughness during physical contact. Here we review the results we recently obtained in the characterization of the contact mechanics of fractal surfaces by depth-sensing indentation. One class of experiments was conducted on organic thin films, load-displacement curves being acquired by atomic force microscopy using custom-designed tips. Another class of experiments focused on well-defined crystalline and mechanically polished ceramic substrates probed by a traditional nanoindenter. We observed the first-loading cycle to be considerably affected by surface roughness. Plastic failure was found to dominate incipient contact while contact stiffness increased on decreasing fractal dimension and roughness. Our findings suggest fractal parameters to drive contact mechanics whenever the penetration depth is kept below the interface width.