The discovery of Kevlar in the late 1960s changed the paradigm completely, and para-aramid fibers and fabrics  became the material of choice for all armor applications. There are traditionally two types of soft armor prepared from woven fabrics - soft body armor and soft armor structures.

Soft body armor is typically used to protect the upper torso by personnel in military and law enforcement agencies worldwide. There are two types of threats - hand gun and pistol ammunition, and piercing fragmented shells and flechette. Bullet resistant vests and jackets are well known examples of soft body armor. 

Soft armor structures include bomb blankets, curtains, liners, backpacks, flexible cases etc. These are typically used to protect structures or equipment or personnel, drapeable and conformable to the protected structure, and also foldable. 

The next stage in the evolution of soft body armor was the development of both woven fabrics and unidirectional nonwoven fabrics using ultra high molecular weight polyethylene yarn. These materials took the performance of body armor a notch higher by offering lighter weight armor, with better trauma protection.  Soft body armor is prepared by stacking multiple plies of flexible fabrics or unidirectional nonwoven fabrics in a proprietary style, and also by hybridising them. Layers of fabrics are stitched and held together using aramid sewing threads. The base fabric is typically treated with a water repellant surfactant, and the entire soft armor pack tightly packed inside a polyester or Nylon tightly woven fabric which is referred to as a outer carrier. These are also heat sealed to prevent moisture from entering the pack. 

Testing standards evolved gradually as well, starting from the first NIJ standard in the US in the 1980s. Ammunition got better defined, testing velocities specified, methods of penetration defined, backface signature on clay included with time. With time, the body armor offered better protection to the wearer. Wider standards as offshoots of the NIJ standard sprouted over time. 

Woven fabrics have gradually got replaced by unidirectional fabrics as they are perceived to offer better trauma protection. 

Disclaimer: Akiro Protech produces woven fabrics, coated fabrics as well as unidirectional tape fabrics using both aramids and polyethylene yarn for end use in the body armor and vehicle armor industries. The above content is a personal view of the author.