A pneumatic bioreactor includes a vessel containing a fluid to be mixed and at least one mixing device driven by gas pressure. A first embodiment includes a floating impeller that rises and falls in the fluid as gas bubbles carry it upward to the surface where the gas is then vented, permitting the impeller to sink in the fluid. The floating impeller may be tethered to a second impeller with a flexible member and pulley. The mixing speed is controlled with electromagnets in the vessel acting upon magnetic material in the impeller or its guides. In another embodiment, floating pistons mix the fluid, pushing it through a mixing plate with one or more apertures. In a third embodiment, the mixing device is a rotating drum with bubble-catching blades and rotating mixing plates with apertures. The top of the vessel for these mixers may include a closed top and sterile filters.