If you stretch a common polyethylene bag under a very strong microscope, you can see that as it fails, the cracks are bridged by fibers. Those are Dyneema starting to form. The stuff is just processed bag material, a chain of carbon atoms, padded out with two chains of hydrogen. I wouldn't call their finishing process annealing, though, just stress-relieving, which happens at a lower temperature. Annealing would soften the rope back into short molecular chains. Spectra fiber is similar.
In composite materials, a big game-changer was aramid fiber, or Kevlar. Unlike most materials, it is very strong and tough in tension, but quite weak in compression, and spectra is even more extreme in that way, and in lower density. If you try to sand a Kevlar surface, the broken fibers pull at the resin and break it up, releasing more length. You have to shave it off, quickly dulling many, many sharp blades.