Check out this fascinating article about piezoelectric transducers baked into smartphone displays, a coming likelihood. Note that the point is not to make better speakers, but to make thinner ones.
The immediate benefits of moving away from traditional magnetic coil speakers are many. The piezoelectric transducer material requires only one millimeter of enclosure thickness, compared to several millimeters for dynamic speakers or linear resonant actuators, enabling a new generation of thinner handheld devices. Yet such transducers can produce the sound quality and the loudness of the best miniature dynamic speakers. They are being made by a few companies, including TDK; others have yet to be announced publicly.
I'm a big fan of technological "talking dogs"—things that become increasingly unpleasant once you get over your amazement at its existence—and have high hopes for piezoelectric transducers.