Si-based optical interconnection is expected to solve the problems caused by electric interconnection with increasing the density of integrated circuits, due to its merits of high speed, high bandwidth, and low consumption. So far, all of the key components except light source of Si-based optical interconnection have been demonstrated. Therefore, the light source has been considered as one of the most important components. Ge and GeSn based on Si have emerged as very promising candidates because of their high compatibility with Si CMOS processing, and the pseudo direct-bandgap characteristic. The energy difference between the direct and indirect bandgap of Ge is only 136 meV at room temperature. Under tensile strain or incorporation with Sn, the energy difference becomes smaller, and even less than zero, which means that Ge or GeSn changes into direct bandgap material. What is more, using large n-type doping to increase the fraction of electrons in valley, we can further increase the luminous efficiency of Ge or GeSn. In this paper, we briefly overview the recent progress that has been reported in the study of Ge and GeSn light emitters for silicon photonics, including theoretical models for calculating the optical gain and loss, several common methods of introducing tensile strain into Ge, methods of increasing the n-type doping density, and the method of fabricating luminescent devices of Ge and GeSn. Finally, we discuss the challenges facing us and the development prospects, in order to have a further understanding of Ge and GeSn light sources. Several breakthroughs have been made in past years, especially in the realizing of lasing from GeSn by optically pumping and Ge by optically and electrically pumping, which makes it possible to fabricate a practical laser used in silicon photonics and CMOS technology.