To be clear, theory is being used here in the scientific sense, not in the colloquial sense of being a hypothesis. The science behind solar sails has been solid since Einstein's earlier discoveries (e.g. what he earned his first Nobel Prize for), when he discovered that light, despite having no mass, nevertheless does have momentum thanks to relativity. From there it's a straight shot towards realizing that you can make something move in space when it's hit by something carrying by momentum, exactly the same as a sail on Earth when it's hit by air particles carrying momentum. Basically it just became a problem of engineering at that point.
Some important limitations to keep in mind with solar sails are that the momentum imparted on them tails off according to an inverse square law, and also that since they have no medium like water to push against (hence no rudder), you can't "tack into the wind" like a sailboat can. However, and this is a very important point, because of the way orbital mechanics works out, and assuming you can adjust your orientation of the sail on the fly, this matters less than you might think, e.g. imagine orienting your sail at apoapsis so that you create a net thrust in the retrograde direction, then you furl or orientate your sail edge-on to the Sun. You end up with an orbit that has a periapsis closer to the Sun (with an apoapsis further out), so you're still traveling inward in some sense, at least for part of your orbit.