Do wormholes exist?

Albert Einstein's general theory of relativity, formulated in 1915, predicted the existence of an expanding Universe, of black holes, and of gravitational waves. In each case, physicists originally believed that these predictions were just mathematical curiosities. But over the past century, each prediction has been confirmed. Could the same be true for wormholes - shortcut connections between two widely separated points in spacetime? They, too, are a possible outcome of Einstein's theory. However, no one has ever observed a wormhole, let alone passed through one. Except in science fiction movies, of course.