The alternative to rebar is making sure your structure is under compression with negligible tension.
(Think of how hard you'd have to shake the Great Pyramid of Giza to make it collapse. That's not concrete obviously, but it too is under compression almost entirely, except for the corbel and lintel ceilings. The proper arches used in Roman concrete construction show that with the right engineering you can push unreinforced concrete pretty damn far. The Pantheon is probably the most impressive example of it. Compare how well it's withstood earthquakes with the Colosseum.)