Magnetic systems in which the single ion ground state is a singlet may exhibit a soft mode phase transition corresponding to a polarization instability of the ground state wavefunction. In this article, theory and experiment for such systems is reviewed and discussed in the context of rare earth metals and intermetallic compounds. The theory is reviewed successively for the idealized singlet‐singlet, and singlet‐triplet models and for real level schemes. The importance of the respective uniaxial, isotropic and typically cubic symmetries is stressed. Inelastic neutron scattering studies of the dynamics in a variety of rare earth singlet ground state systems are discussed. Particular attention is given to three representative systems: TmSb, a model Van Vleck paramagnet, (PrxLa1−x)3Tl, a family of alloys exhibiting a delicately balanced induced moment ordering for x > 0.93, and TbSb, a strongly over‐critical antiferromagnet. In these latter two systems the T = 0 properties are well understood but existing RP...