[enriquto]

Besides seeing through clouds and at night, you can often correlate images taken at different times and detect tiny movements (of fractions of a millimeter). This technique is called "interferometry". You can observe minute movements of large swaths of terrain; this is impossible with optical images.

[notahacker]

As a relevant commercial example, you can see patterns of subsidence which indicate a sinkhole is about to form near your mine. You're probably only looking at a relatively small area but it's unlikely to be evident from optical images.

As an indication of how sensitive it is, you can use SAR interferometry to see where Crossrail tunnels have been bored under London, despite the elevation change of the buildings and roads on top being too small to have had any impact on their structural integrity. The caveat is that this level of sensitivity you get when looking at smooth, undisturbed surfaces like the roofs of buildings isn't matched when you're looking at fields with growth and soil movement

[enriquto]

> looking at smooth, undisturbed surfaces like the roofs of buildings

a flat roof (with fine enough texture) will be reflective thus invisible. What you see are precisely tiny "corner" reflectors formed by large enough gravel, rocks and building structures. On a mountainous area, as long as you have some rocks and gravel here and there, you are still able to find correlations--and thus interferences. Of course, if all you have is wet mud and vegetation there's nothing to do, but this is not often the case. In a region of special interest like near a mine, people often install ad-hoc corner reflectors at calibrated positions.