The challenges posed by the scaling of Silicon (Si) devices make mandatory the study of new materials to overcome the physical limitations of the Si. Germanium (Ge) was actually used in the first transistors but was then abandoned in favour of Si due to difficulties in processing Ge Oxide. However, the introduction of high-K gate dielectrics makes the use of Ge possible in an advanced technology. Its benefits for MOSFET applications are important: better transport properties than with Silicon hence higher saturation currents; lower band gap hence lower supply voltages and lower power dissipation and a lattice parameter compatible with Gallium Arsenide (GaAs) epitaxy. These are the main reasons why, during the last 4 years, the interest in Ge and Ge-On-Insulator (GeOI) substrates fabrication and properties has grown. This paper is a review of the different types of Ge and GeOI substrates, their critical aspects and their new potential applications.