The modern hang gliding sport went through an early, severe crash-n-burn period. I took hang glider lessons back in those days, but never progressed beyond low flights down a "bunny hill." I went off gyro-ing instead.
The Rogallo wing was somewhat similar to the Lilienthal. Both have unsupported trailing edges and fabric wing surfaces limber enough to change shape in flight. At higher speeds, such wings can go into a "luff dive" that is statically divergent -- it gets harder and harder to pull out with just weight-shift as your airspeed builds. The source of the problem is center-of-pressure shift; the wing's aerodynamic center shifts aft, enabled by the soft wing surface. The effect is like adding a bunch of ballast to the nose: lawn dart! There is some evidence that this phenomenon is what caused Otto Lilienthal's fatal crash.
The hang-glider industry cleaned up its act as the fatalities mounted, opting for more rigid wings, higher aspect ratio and some wing-warping to augment weight shifting. Today's trike wings and hang gliders are the (safer) result.