[cushychicken]

Tons of applications and uses in electronic warfare and electronic intelligence gathering.

Also forms a lot of the basis of RADAR, though that's a separate use case.

To oversimplify: SDR allows you to build a radio based around math instead of complex electronics - or, at least fewer complex electronics. It sacrifices a bit of performance but confers a lot of the advantages you get in other software systems - updates, reconfigurability, etc.