The controlled application of strain in crystalline semiconductors can be used to modify their basic physical properties to enhance performance in electronic and photonic device applications. In germanium, tensile strain can even be used to change the nature of the fundamental energy band gap from indirect to direct, thereby dramatically increasing the interband radiative efficiency and allowing population inversion and optical gain. For biaxial tension, the required strain levels (around 2%) are physically accessible but necessitate the use of very thin crystals. A particularly promising materials platform in this respect is provided by Ge nanomembranes, that is, single-crystal sheets with nanoscale thicknesses that are either completely released from or partially suspended over their native substrates. Using this approach, Ge tensilely strained beyond the expected threshold for direct-band gap behavior has recently been demonstrated, together with strong strain-enhanced photoluminescence and evidence of population inversion. We review the basic properties, state of the art, and prospects of tensilely strained Ge for infrared photonic applications.