The general concept of jamming in disordered systems will be introduced, emphasising the similarities between the jamming behaviour of a physically diverse range of materials. For the disordered particle packings under study, there are pronounced structural signatures of jamming that are reflected in the properties of granular materials. Of particular interest is an analysis of the vibrational spectrum near the jamming transition, which shares features seen in low-temperature glasses. Surprisingly, the low-frequency normal modes do not conform to typical phonon behaviour making the jamming transition not only an unusual type of phase transition but also an unusual type of solid.