There are 2 main materials for body armor.
UHMWPE
The first material is UHMWPE which is an ultra-high-molecular-weight polyethylene, which is a chemical polymerization process in which monomers are converted to polymers. UHMWPE is VERY strong versus its weight, and has a high resistance to both ballistic, sharp edged and pointed instruments. UHMWPE is not only used in bullet proof and stab proof vests, but also in clothing, fishing lines, cut resistant gloves, aircraft containers, sports equipment, clothes, etc.
Dyneema from DSM
Dyneema is one of the most used polyethylene materials in bullet proof vests and according to DSM itself, Dyneema is up to 15 times stronger than steel, and 40% stronger than aramid fibers when considering the weight versus the strength. DSM has many different Dyneema fibers, which all have different properties.
Aramid
Aramid is a synthetic fiber that was created back in the 1960s by Stephanie Kwolek. The fiber is known especially from Dupont Kevlar, which were the first company with a commercial version for bullet proof vests, followed by Twaron from Teijin. Aramid is used in bullet proof vests and stab proof vests, as the material is very strong and flexible, and has proven to be stable and safe after many years of use.