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Experimental investigations in the field of longitudinal wave propagation in beams are plentiful; however, experimental studies of flexural wave propagation problems are scarce and are restricted mainly to uniform and infinite structures where the effects of reflected waves are not generally included. This review is mostly restricted to low velocity impact and does not cover the so-called high velocity impact such as those of bullets and explosives. In addition to a brief survey of classical work related to impact, this article covers publications related to experimental studies of longitudinal and flexural elastic waves due to impact. This includes the longitudinal, central as well as eccentric impact and transverse impact of two bars and the impact achieved by sphere impinging on a beam. Many workers used experimental findings to study the adequacy of various theoretical solutions of the wave propagation problem such as those by Pochhammer and Chree, Euler–Bernoulli, and the Timoshenko beam theory. The revival of interest in the recent years is due to, among other things, the advancement of experimental equipment and measurement techniques for data acquisition of stress waves and associated signals. An important application of transient waves is their use for the determination of material properties under various loading conditions and strain rates that can be studied by the split Hopkinson pressure bar techniques. The problem of longitudinal and flexural waves in bars with discontinuities of cross section are covered, and some publications on fracture of materials due to bending waves are also included. Experimental investigations demonstrate the effect of abrupt change of cross section and/or material properties on reflected and transmitted waves where reflections are to be taken into consideration when estimating the level of stresses and strains in finite beam with discontinuities. In the field of flexural wave propagation, comparison of theoretical predictions with experimental results verified and validated the adequacy of the Timoshenko theory for the determination of bending strain in finite structures, a one-dimensional theory that takes into account the effect of shear deformation and rotatory inertia.