Fibres made from regenerated cellulose aren't new. They were first developed in the late 1800s and Courtaulds created the first viscose rayon, often called artificial silk, in 1905.
Wood, cotton linters(the short fibres that are too short to spin into cotton yarn), bamboo, nettles etc. can all be reduced to a pulp that's treated with chemicals to create a thick viscose liquid. This thick syrupy liquid is forced through a spinneret(think pepper pot with holes too small to see by the naked eye) to form fine strands that are dried and spun to make yarns.
The most important developments have been in the manufacturing process. The most environmentally friendly fibres like Lyocell(trade name Tencel) is made in closed loop systems where the chemicals are reused in the manufacturing process.
A really exciting development is using the waste from growing vegatables to make viscose fibres, not only are the chemicals reused, but the nutrient rich water is used to irrigate the crops...............