[azernik]

They are actually quite visible - their accretion disks (matter falling into the black hole) are very hot and radiate on a broad range of frequencies.

[marcosdumay]

An accretion disk is not a black hole. Current physics have no other explanation for the disks, but it does not mean that the black holes are really there.

There is also some lack of precision on the LIGO experiment that does not invalidate all reasonable alternative explanations.

As people already said, the evident is overwhelming on the side of black holes existing. But we don't have any definitive measurement of them.

[azernik]

We have direct proof of:

* extremely large masses

* in very small volumes

* that are not, themselves, emitting anything

It could be many things, but they pretty much all fit the definition of "black hole".

[WJW]

I think this is as definitive a proof we'll get until we get close enough to directly measure Hawking radiation. Of course, by that time we should also be close enough to "see" the black hole directly...