The theoretical prediction of black holes dates back to 1916, when Karl Schwarzschild proposed a solution to Einstein's field equations that were part of his general theory of relativity. General relativity is arguably the most robust theory in physics - that being said, general relativity introduces some tension with the other most robust theory in physics, namely quantum mechanics and the Standard Model. These two theories are largely accepted to be accurate and correct, and since they predict different phenomena at different length scales, most scientists have no trouble subscribing to both.
With respect to "direct observation" of a black hole, astronomers at the Event Horizon Telescope successfully reconstructed pictures of a black hole using light in the visible spectrum. But to be fair, this comes after decades of overwhelming experimental evidence of black holes + GR. The EHT result probably received the media attention it did because it is easily interpretable as nice lil JPEG, rather than a 12-page paper with dense plots and LaTeX.
With respect to "direct observation" of a black hole, astronomers at the Event Horizon Telescope successfully reconstructed pictures of a black hole using light in the visible spectrum. But to be fair, this comes after decades of overwhelming experimental evidence of black holes + GR. The EHT result probably received the media attention it did because it is easily interpretable as nice lil JPEG, rather than a 12-page paper with dense plots and LaTeX.
See https://en.wikipedia.org/wiki/Tests_of_general_relativity