Two startling ideas about wholly different classes of objects emerged from general relativity: black holes and wormholes. For over half a century black holes have grown in importance, with many convincing candidates in the sky and a vast range of theoretical support. "Einstein bridges" as they were first called, emerged in the 1930s, yet have not met with nearly the attention they deserve. We still don't know if any were made in the early universe. That seems by far the easiest way to find one‹inherit it from the Big Bang‹because to be stable they demand exotic matter. Matt Visser's Lorentzian Wormholes (1996) details the many types of wormholes allowed by theory. It's an impressive range, mostly unexplored theoretically.
If they do exist, they could lead to interstellar travel--indeed, to instantaneous access to points at the far range of the universe. They would also confirm both general relativity and the discovery of exotic matter. But curiously little thought seems given to detecting wormholes, or theorizing about how small, stable ones might have evolved since the early universe. Several co-authors and I proposed using the Massive Compact Halo Object (MACHO) searches to reveal a special class--"negative mass" wormholes--since they would appear as sharp, two-peaked optical features, due to gravitational lensing (Physical Review D 51, p3117-20, 1995) So far all the two peaked cases found have been attributed to binary stars or companion planets, though the data fits are not very close.
Surely there could be other ways to see such exotic objects. Some thought and calculations about wormhole evolution might produce a checkable prediction, as a sidelight to an existing search. Further thought is needed about the implications that extra dimensions from string theory will have on wormholes. It seems theoretically plausible that the inflationary phase of the early universe might have made negative mass string loops framing stable Visser-type wormholes.
Perhaps wormholes do not exist. A plausible search that yielded nothing would still be a result, because we could learn something about the possibility of exotic matter. A positive result, especially detection of a wormhole we could reach with spacecraft, could change human history.