An ornithopter is an aircraft that flies by moving its wings: flapping like a bird's or vibrating like an insect's. They're scientifically plausible and some striking implementations at small scales exist, but ones large enough to transport people (while demonstrated) run into extremely difficult problems of materials science and power efficiency. How feasible are the fast, manoeverable, heavy-loaded ones depicted in Dune?
From an engineering standpoint, we find two major limitations on achieving human flight modeled after birds. These are the ability to translate energy into thrust using these flapping wings and then the structural limitations. The purpose of the flapping wing on a bird, insect, or ornithopter is to create thrust. The body, after being thrusted forward, can sustain flight by simple aerodynamic manipulation through wing shape, the way it has been done for decades. The flapping motion moves air, imparting momentum on the body creating this thrusting force. This means that we would have to design wings that could flap at speeds that would be able to sustain the thrust force to keep the aircraft airborne while being structurally sound and as light as possible, a task easier said than done. Then comes the issue of hovering
A related problem: how to you make a giant flappy aircraft not look ridiculous? David Lynch and John Harrison at SyFy, you'll recall, simply opted not to even try putting true ornithopters in the 1984 and 2000 productions, instead giving the aircraft baroque avian or insect stylings. Denis Villeneuve, with a $170m budget and the benefit of better computer graphics, went for the insect vibtratey type and pulled it off very well.