Since the birth of astrophysics, astronomers have been using free-space optics to analyze light falling on Earth. In the future however, thanks to the advances in photonics and nanoscience/nanotechnology, much of the manipulation of light might be carried out using not optics but confined waveguides, or circuits, on a chip. This new generation of instruments will be not only extremely compact, but also powerful in performance because the integration enables a greater degree of multiplexing. The benefit is especially profound for space- or air-borne observatories, where size, weight, and mechanical reliability are of top priority. Recently, several groups around the world are trying to integrate ultra-wideband (UWB), low-resolution spectrometers for millimeter-submillimeter waves onto microchips, using superconducting microelectronics. The scope of this Paper is to provide a general introduction and a review of the state-of-the-art of this rapidly advancing field.