These notes summarise the lectures given at the International School of Physics “Enrico Fermi”, in July 2017 at Varenna (Italy), about the use of transfer reactions to extract spectroscopic information on nuclei far from the valley of stability. Transfer reactions as a probe of nuclear structure have re-gained importance in the last 20 years with the development of good-quality beams of unstable nuclei, and thus the possibility of carrying out reaction studies in inverse kinematics. After a short introduction about the general properties of nuclear reactions and transfer reactions in particular, the notes discuss the experimental challenges related to the use of radioactive ion beams. The main part is then dedicated to the presentation of a number of selected experimental studies. The focus lies on the impact of those studies on our understanding of the nuclear structure and the features of the underlying nucleon-nucleon interaction. The topics touched upon are: shell evolution in light nuclei at N = 8, the disappearance of the N = 20 shell closure and the emergence of another shell gap at N = 16; the spin-orbit term of the nucleon-nucleon interaction and the changes in its strength in exotic nuclei; the microscopic origin of shape coexistence in low-lying 0⁺ states, in the neutron rich Mg and Ni regions. We conclude with a brief reflection on the present developments and challenges for experiments and theory in this field.