The background and motivation of the non-silicon microelectronics, in which the non-silicon channel materials are used to realize the CMOS integrated circuits, are introduced in this paper. As the typical non-silicon microeletronic devices, Germanium (Ge) and Germanium-Tin (GeSn) metal-oxide-semiconductor field-effect transistor (MOSFET) and tunneling field-effect transistor (TFET) are reviewed. Ge and GeSn are the promising candidate materials for the realization of high mobility channel CMOS devices owing to their high carrier mobilities and easy integration on Si platform. GeSn can transit from indirect to direct bandgap material by tunning Sn composition thus achieving the high band-to-band tunneling generation rate. Theory and experimental results proved that GeSn can be used to fabricate the high performance TFETs. A series of key problems including the growth of materials, surface passivation, gate-stack layer, source-drain engineering, strain engineering, and device reliability are discussed.Germanium, Germanium-Tin, field-effect transistor (FET), mobility, band-to-band tunneling