A brief review of recent work performed at the Institute of Spectroscopy of the Russian Academy of Sciences (ISAS) by high-resolution broad-band optical Fourier spectroscopy on the study of crystals doped with rare-earth ions is presented. The results of investigation of inhomogeneous broadening and fine structure of lines in the absorption and luminescence spectra of crystals with rare-earth ions caused by random deformations, isotopic structure in the luminescence spectra associated with matrix isotopes, anticrossings of hyperfine levels in the magnetic field are presented. It is shown that the hyperfine structure in the luminescence spectra can be used to realize a luminescent thermometer for the ultra-low temperature region.