The principal properties of the transversity amplitudes (i.e. amplitudes with spins projected on the normal to the reaction plane) are presented. The properties which are important for applications, as the simplicity of crossing relations and the behaviour under spatial reflections are discussed in detail. The applications to the study of behaviour of scattering amplitudes at thresholds and pseudothresholds and to the description of spin correlations in decay distributions are also presented. Finally many other applications (including those proposed by other authors) are shortly discussed.