Because their thickness dimension is very small compared with other dimensions, the one-dimensional (1D) nanostructures (such as nanowire, nanotube, and nanobelt) and two-dimensional (2D) nanostructures (such as graphene) are highly prone to bend. Because of their large bending flexurality, the 1D and 2D nanostructures exhibit different contact behavior from those chunky ones. Without considering the flexurality effect, the analysis on the experimental data of 1D and 2D nanostructures can lead to different and even contradicting results/conclusions on their mechanical properties. One focus of this chapter is on what can go wrong in the indentation and three-point bending tests of 1D nanostructures if the flexurality effect is not accounted. At the same time, the 1D and 2D nanostructures also exhibit abnormal friction behavior. The assumptions of the classical contact are reviewed, and their possible deficiencies and difficulties of being used to analyze the contact and friction of 1D/2D nanostructures are also discussed.