"People for thousands of years have been developing bullet resistant armor"
Present day vests do their job. In fact they save approximately 3,000 lives per year. Currently, body armor is comprised of non-woven and/or woven fabrics. There are specific level vests for particular areas of combat.
Although, there are competitors with more advanced technology such as Liquid Armour (using non-Newtonian fluids) which is extremely heavy and Dragon Skin Armour (Dragon Skin Armour has not passed inspection by the army)