In recent years, Ge has emerged as one of the most promising materials toward next-generation high-performance and low-power-consumption optoelectronic devices. Moreover, SiGe/Ge heterostructures, consisting of strained SiGe with high Ge contents and Ge, have high potential for various applications. In terms of crystal orientations, there are various attractive choices for Ge and Ge-rich SiGe differently from Si. Particularly, the (111) orientation is very attractive for spintronics applications owing to capability of lattice matched epitaxial growth of high-quality ferromagnetic materials on the Ge(111) and SiGe(111). To create the SiGe/Ge heterostructures on the Si substrate, high quality Ge virtual substrates firstly have to be formed on the Si. The so-called Ge-on-Si is simple but very important templates for various applications, such as Ge-MOSFETs, LEDs, LDs, photo detectors, micro structures and Ge-on-Insulator (GOI) wafers etc. Especially the tensile strain induced in the Ge due to the thermal mismatch between the Ge and Si plays very important roles. For example, very efficient light emission can be obtained through strain-induced Γ-valley shift and resultant increase in the direct transition probabilities. We fabricated both Ge-on-Si(100) and Ge-on-Si(111) p-i-n LEDs and strong room-temperature EL emissions were obtained [1]. Epitaxial growth of the high quality strained SiGe on the Ge-on-Si is the most important for strain engineering of SiGe/Ge heterostrucutures. As the growth of the strained layer is limited by the critical thickness, we systematically investigated the critical thickness of the strained SiGe and clarified that it depends on the crystal orientations [2]. It was also shown that the critical thickness is markedly reduced when grown on the Ge-on-Si compared to the Ge substrate due to dislocations in the Ge-on-Si. We proposed to grow the SiGe on the Ge-on-Si on which the mesa patterning is performed. As a result, the critical thickness is drastically increased owing to the suppression of defect generation and propagation [3]. This patterning method enables us to increase the strained layer thickness and highly widen potential applicabilities of the strained SiGe/Ge heterostructures. One of the attractive applications is strained SiGe/Ge multi quantum wells (MQWs). We obtained strong roome temperature light emissions from the relatively thick MQWs formed on the Ge-on-Si (111) and Si(100) with patterning. Based on the Ge-on-Si, the larger tensile strain can be induced by the fabrication of microbridge structures, where the freestanding Ge is realized and elastic tensile stress is applied to the narrow microbridge area via the local strain relaxation of large pad areas sandwiching the bridge. In many reports, standard Si(100) substrates have been used with the bridge direction set to be <001> direction, whereas the Γ-valley shift via the tensile strain is expected to be the largest with the <111> directional uniaxial strain [4]. We attempt to fabricate the Ge microbridge along the <111> direction on the Ge-on-Si(110) substrate and very strong room-temperature PL was obtained. Moreover, when microbridge side walls are formed vertical, the generated light is well reflected by the side walls and very strong resonant light emissions are observed. Technically, the selective wet-etching of the underlying Si of the Ge-on-Si is a key process of importance to fabricate completely freestanding structures. As the crystal orientation highly affects the etching rate, a choice of the orientation is very important. Additionally, we are attempting other fabrication methods. One is making many holes in the pad areas, which enables to enhance the under-etching. Use of Ge-on-SOI or Ge-on-Insulator (GOI) substrates is another way to facilitate the under-etching as the buried oxide can be easily removed by the fast etching. Moreover, we show recent results on SiGe/Ge heterostructure imbedded microbridge, where the light emission wavelength becomes controllable and emission efficiency can be enhanced owing to the strain and band engineering.[1] K. Yamada et al. Appl. Phys. Express 14, 045504 (2021). [2] M. M. Alam, Appl. Phys. Express 12, 081005 (2019). [3] Y. Wagatsuma et al. Appl. Phys. Express 14, 025502 (2021). [4] H. Tahini et al. J. Phys. Condens. Matter 24, 195802 (2012).