Integrated silicon nanophotonics has rapidly established itself as intriguing research field, whose outlets impact numerous facets of daily life. Indeed, nanophotonics has propelled many advances in optoelectronics, information and communication technologies, sensing and energy, to name a few. Silicon nanophotonics aims to deliver compact and high-performance components based on semiconductor chips leveraging mature fabrication routines already developed within the modern microelectronics. However, the silicon indirect bandgap, the centrosymmetric nature of its lattice and its wide transparency window across optical telecommunication wavebands hamper the realization of essential functionalities, including efficient light generation/amplification, fast electro-optical modulation, and reliable photodetection. Germanium, a well-established complement material in silicon chip industry, has a quasi-direct energy band structure in this wavelength domain. Germanium and its alloys are thus the most suitable candidates for active functions, i.e. bringing them to close to the silicon family of nanophotonic devices. Along with recent advances in silicon-germanium-based lasers and modulators, shortwave-infrared receivers are also key photonic chip elements to tackle cost, speed and energy consumption challenges of exponentially growing data traffics within next-generation systems and networks. Herein, we provide a detailed overview on the latest development in nanophotonic receivers based on silicon and germanium, including material processing, integration and diversity of device designs and arrangements. Our Review also emphasizes surging applications in optoelectronics and communications and concludes with challenges and perspectives potentially encountered in the foreseeable future.