Low-temperature paramagnets are a class of spin systems that remain in a disordered paramagnetic state down to the lowest temperatures despite the presence of noticeable spin-spin exchange coupling. The magnetic properties of these systems at low temperatures are due to collective spin excitations, and, in a magnetic field, such spin systems can demonstrate field-induced antiferromagnetic ordering. Magnetic resonance allows studying the details of the excitation spectrum in the paramagnetic low-field and ordered high-field phases of low-temperature paramagnets, revealing the fine structure of the spectrum of collective excitations, details of the interaction between excitations, changes in the excitation spectrum induced by the magnetic field, and the emergence of non-Goldstone modes of spin dynamics in high-field ordered phases.