Modern methods for determining the hardness, Young’s modulus, elastic recovery, adhesive/cohesive strength, friction coefficient, and wear resistance of thin films, coatings, multilayer materials, and bulk materials are considered. The experimental data obtained in instrumented indentation, instrumented scratching, and tribological tests of nanostructured and quasicrystalline coatings and composite materials are analyzed. It is noted that the elastic recovery of a number of advanced materials is higher than the elastic recovery of metal alloys by a factor of 2–3. The coefficients of sliding friction of sintered samples and thin films containing Al-Cu-Fe quasicrystals are found to be relatively low. An increase in the fraction of quasicrystalline particles to 30% in composites with an aluminum matrix leads to an increase in the wear resistance.