The solid state exhibits a fascinating variety of phases, which can be stabilized by the variation of external parameters such as temperature, magnetic field and pressure. Until recently, numerical analysis of magnetic and/or orbital phases with collective excitations on a periodic lattice tended to be done on a case-by-case basis. Nowadays dynamical matrix diagonalization (DMD) has become an important and powerful standard method for the calculation of dispersive modes. The application of DMD to the interpretation of inelastic neutron scattering (INS) data on dispersive magnetic excitations is reviewed. A methodical survey of calculations employing spin-orbit and intermediate coupling schemes is illustrated by examples. These are taken from recent work on rare earth, actinide and transition metal compounds and demonstrate the application of the formalism developed.