Nanoscale materials that possess ultra-small dimensions or consist of a single two-dimensional layer of atoms can exhibit novel physical properties that may lead to new functionalities. Such properties can arise from the high surface area, which yields extraordinary chemical and electronic sensitivity at their interfaces. However, these materials also can display entirely new physical phenomena that are not present in larger systems. This talk will examine a number of examples as well as discuss how x-ray and neutron scattering investigations can provide unique insight into these materials. An overview of the x-ray and neutron scattering facilities for these types of studies will also be presented.