Inelastic neutron scatting (INS) is a fundamental microscopic technique to study the energy and momentum dependence of excitations related to lattice-, spin-, and orbital degrees of freedom in solids. Quasi-elastic neutron scattering (QENS) is a closely related form of INS applied to study excitations related to random interactions such as diffusive motion in liquids, biomolecular dynamics or paramagnetic spin-fluctuations. We will review the principles of INS and QENS, some basic instrumental setups and methods. As practical examples we briefly spotlight INS and QENS studies of some rare earth intermetallic compounds with respect to nuclear INS (e.g. phonon excitations) and magnetic INS and QENS related to crystalline electric field effects and paramagnetic fluctuations, respectively.