Due to their large conduction-band offsets, GaN/AlGaN quantum wells can accommodate intersubband transitions at record short wavelengths throughout the mid-infrared and into the near-infrared spectral regions. As a result, they are currently the subject of extensive research efforts aimed at extending the spectral reach and functionality of intersubband optoelectronic devices. Here we review our recent work in this area, based on GaN/AlGaN quantum-well samples grown by molecular beam epitaxy on sapphire substrates. In particular, we have investigated the intersubband absorption properties of a wide range of structures, including isolated and coupled quantum wells. Furthermore, we have developed a new class of ultrafast all-optical switching devices, based on intersubband cross-absorption saturation in GaN/AlGaN quantum-well waveguides operating at fiber-optic communication wavelengths. Strong self-phase modulation of ultrafast optical pulses has also been measured in these waveguides, revealing a large refractive-index nonlinearity which is related to the same intersubband carrier dynamics. Finally, we have demonstrated optically pumped intersubband light emission from GaN/AlN quantum wells resonantly excited with a pulsed OPO. The measured room-temperature output spectra are peaked near 2 μm, which represents a new record for the shortest intersubband emission wavelength from any quantum-well materials system.