Theoretical and experimental results are presented on the diagnostics of erythrocyte mechanical properties by two recently emerged techniques: Flicker Spectroscopy (FS) and Dielectro-Deformation (DD). FS allows us to monitor the bending modulus of a cell membrane and the viscosity of a cell interior, while DD allows monitoring of the shear modulus and the surface viscosity of a cell membrane. All four moduli are very sensitive to physiological state and pathological processes in erythrocytes, as well as to various environmental changes. The correct evaluation of these moduli or their changes from the measured curves requires elaborate theory. This theory should adequately take into account rather complex geometrical, mechanical, and electric characteristics of erythrocyte, as well as instrumental function of the measuring optical set-up. The approximate models, which give analytical solutions are formulated, namely, the modified planar model of erythrocyte flickering, and the general dynamic equation of erythrocyte dielectro-deformations. The instrumental function is introduced and its role is discussed. The flicker spectra are measured in a broad frequency range 0.05 divided by 500 Hz using different optical set-ups. The results are compared with the theory. The amplitude-frequency characteristics of forced dielectro- deformational oscillations of erythrocyte are measured also, giving the characteristic time of viscoelastic relaxation of its shape. Some problems of diagnostic applications of FS and DD are discussed.