Harnessing energy from black holes usually known as the Penrose process, because Roger Penrose devised how it might work in theory.
The Penrose process (also called Penrose mechanism) is a process theorised by Roger Penrose wherein energy can be extracted from a rotating black hole.1 That extraction is made possible because the rotational energy of the black hole is located not inside the event horizon of the black hole, but on the outside of it in a region of the Kerr spacetime called the ergosphere, a region in which a particle is necessarily propelled in locomotive concurrence with the rotating spacetime. All objects in the ergosphere become dragged by a rotating spacetime. In the process, a lump of matter enters into the ergosphere of the black hole, and once it enters the ergosphere, it is split into two. The momentum of the two pieces of matter can be arranged so that one piece escapes to infinity, whilst the other falls past the outer event horizon into the hole. The escaping piece of matter can possibly have greater mass-energy than the original infalling piece of matter, whereas the infalling piece has negative mass-energy. In summary, the process results in a decrease in the angular momentum of the black hole, and that reduction corresponds to a transference of energy whereby the momentum lost is converted to energy extracted.
The maximum amount of energy gain possible for a single particle via
this process is 20.7%. The process obeys the laws of black hole
mechanics. A consequence of these laws is that if the process is
performed repeatedly, the black hole can eventually lose all of its
angular momentum, becoming non-rotating, i.e. a Schwarzschild black
hole. In this case the theoretical maximum energy that can be
extracted from a black hole is 29% its original mass. Larger
efficiencies are possible for charged rotating black holes.
A similar question was asked on the Physics Stack Exchange How would a black hole power plant work. It has two answers dealing with extracting rotational energy and using a black hole as a spaceship thruster (an idea whose time hasn't exactly come).
The simple answer is yes, puny humans have devised theoretical mechanisms to extract energy from black holes. The rest is mere engineering.