Nonlinear generation of odd harmonics of the electromagnetic pumping field in a fully ionized plasma is briefly surveyed. Two threshold bifurcation properties of the harmonics are discussed, viz. the splitting of the peak of their intensity as a function of the degree of circular polarization of the pumping field and, at a somewhat higher threshold, the emergence of nonzero-intensity harmonics with complete circular polarization in a pumping field with a partial circular polarization.