It's relatively easy to get something big and heavy to fly. With enough equipment, it's possible to load the object with lots of energy to power the flight, specialized parts to control it, and the computers (or people) needed to direct the flight. But things get challenging as you make things smaller, and it gets harder to squeeze all the requisite parts into an ever-shrinking space. In that, nature has us beat, since something like a fruit fly crams all the energy, control systems, and specialized hardware into an extremely compact form.
We may not be at fruit fly level yet, but researchers are giving the insects some competition. Today's issue of Science reports on miniature flying robots that aren't much bigger than a coin. The power and control are handled externally, but the tiny robots can still perform basic maneuvers, and they have enough lift to spare that they could fly under their own power for a few minutes if the right power storage were developed.
The authors are all from the Wyss Institute for Biologically Inspired Engineering at Harvard, and they clearly find insects inspirational, noting that, despite their simple nervous systems, "flying insects are able to perform sophisticated aerodynamic feats such as deftly avoiding a striking hand." So they set out to build their own.