Aside from local communications here on Earth, high bandwidth to deep space missions would open up many possibilities for astronomy. Multiple telescopes can be linked and a view synthesized in software. Greater physical distance between the linked telescopes translates into increased angular resolution. For local objects, you also get parallax information, giving depth perception, just like with two eyes instead of one. In theory, two telescopes in an orbit around the sun, spaced half an orbit apart, would have the angular resolution of a telescope with a mirror of the same diameter as the orbit. Perhaps 10 billion km across, if they were placed at the outer reaches of the solar system.
It has been done here on Earth with multiple telescopes, and with Earth-orbiting satellites. Often very short observations recorded to bulk storage media, then compared slower than real-time after. To do such observations at microwave or far infrared wavelengths would require many gigabits of bandwidth per second of observation. Infrared or optical is terabits or petabits per second. These numbers are no longer as incomprehensible as they used to be.
It has been done here on Earth with multiple telescopes, and with Earth-orbiting satellites. Often very short observations recorded to bulk storage media, then compared slower than real-time after. To do such observations at microwave or far infrared wavelengths would require many gigabits of bandwidth per second of observation. Infrared or optical is terabits or petabits per second. These numbers are no longer as incomprehensible as they used to be.