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An investigation of spectra, radiative and autoionization characteristics for the rare-earth elements is of a great interest as for development atomic spectroscopy as different applications in plasma chemistry, astrophysics, laser physics, quantum electronics etc. We present and review the results of studying spectra and autoionization resonance characteristics of a few lanthanide elements (ytterbium and thulium). Computing the spectra and autoionization resonance parameters is carried out within the relativistic many-body perturbation theory (RMBPT) and generalized relativistic energy approach. The accurate results on the autoionization resonance energies and widths are presented with correct accounting for the exchange-correlation and relativistic corrections and compared with other available theoretical and experimental data. In this chapter, we present a brief review of the theoretical and experimental works on spectroscopy of some lanthanide atoms. Spectroscopy of the Rydberg autoionization resonances in rare-earth atoms in an external electromagnetic field is expected to be very complex and unusual.

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