The last few years have seen dramatic advances in the growth, fabrication and characterization of low-dimensional materials and nanostructures. Most studies of these artificially engineered materials have been driven by their potential for device applications that involve smaller and smaller physical dimensions. In particular, the dynamical properties of these materials are of fundamental interest for the devices that involve high-frequency operation and/or switching. Consequently, the different excitations, vibrational, magnetic, optical, electronic, and so on, need to be understood from the perspective of how their properties are modified in finite structures, especially on the nanometre length scale due to the presence of surfaces and interfaces.