The paper gives a brief overview of nonlocal theories in solid mechanics from the viewpoint of wave motion. The influence of two essential qualities of solids - nonlocality and nonlinearity - is discussed. The effects of microstructure are analysed in order to understand their role in nonlocal theories. Various models are specified on the level of one-dimensional unidirectional motion in order to achieve mathematical clarity of interpreting physical phenomena. Three main types of evolution equations are shown to govern deformation waves under such assumptions. Based on the dispersion analysis, weak, true, and strong nonlocality are distinguished.