The study of isotope shifts and hyperfine effects in dielectronic recombination (DR) resonance spectra strikes a conceptually new path for investigations of nuclear properties such as charge radius, spin, magnetic moment of nuclei or lifetimes of long-lived excited nuclear states. A series of DR experiments with heavy three-electron ions (Li-like) was performed at the heavy-ion storage ring ESR of the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany. In a pilot experiment the two stable isotopes A=142 and A=150 of neodymium ^ANd⁵⁷⁺ were investigated. From the displacement of DR resonances the isotope shifts δE^142,150(2s - 2P_l/2) 40.2(3)(6) meV and δE^142,150(2s - 2p_3/2) 42.3(12)(20) meV for 2s - 2P_j transitions of the Li-like ions have been obtained. An evaluation within a full QED framework yielded a change in the mean-square charge radius of ^142,150δ(r²) -1.36(1)(3) fm². At GSI, in addition to stable isotopes, in-flight synthesized radioisotopes can be studied as well. The production of radioisotopes of interest, the subsequent separation in the storage ring ESR and first DR experiments with the exotic nuclei ²³⁷U⁸⁹⁺ and ²³⁴Pa⁸⁸⁺ (Z=91) are presented. The paper is concluded with a brief outlook at future DR experiments with heavy radioisotopes at the ESR.