Flies are among the most agile flying creatures on Earth. To mimic this aerial prowess in a similarly sized robot requires tiny, high-efficiency mechanical components that pose miniaturization challenges governed by force-scaling laws, suggesting unconventional solutions for propulsion, actuation, and manufacturing. To this end, we developed high-power-density piezoelectric flight muscles and a manufacturing methodology capable of rapidly prototyping articulated, flexure-based sub-millimeter mechanisms. We built an 80-milligram, insect-scale, flapping-wing robot modeled loosely on the morphology of flies. Using a modular approach to flight control that relies on limited information about the robot's dynamics, we demonstrated tethered but unconstrained stable hovering and basic controlled flight maneuvers. The result validates a sufficient suite of innovations for achieving artificial, insect-like flight.