Modern armor is bullet resistant, not bulletproof. With enough ballistic energy, soft armor can be pierced. This means that body armor is a balanced compromise, with wearability and comfort balanced against effectiveness. The result is a vest that is thin, light and comfortable enough that officers will wear it, even in the warmer climates, and still efficient enough to stop the most likely bullets. One can always build a heavier vest, but if it is uncomfortable enough, officers won't wear it. Then all benefit is lost.
Modern armor does not deflect bullets. Rather, the armor catches the bullet, dispersing its energy across a wider area of fabric, thereby preventing penetration. Think of the difference between a thrown baseball and a hunting arrow launched from a bow. Upon impact, the arrow focuses all of its energy on a very small part of the target. As the arrow's point enters the target, the arrowhead's shape opens a larger wound, which allows the bulk of the projectile to pass through.
Conversely, a baseball thrown with the same energy behind it will hit a larger area of the target's surface, but the energy is spread over a larger area; the energy is dissipated without penetration.
Early soft body armor was made of nylon (a polyamide) and had fairly poor ballistic performance. It required many thick layers for increased effectiveness. Today, the high strength fibers that are used in the production of bullet resistant panels for soft body armor are of two primary types, 1) high performance polyethylene fibers, otherwise known as HPPE, and 2) aramid fibers. Honeywell's Spectra® and DSM's Dyneema® are HPPE fibers. DuPont's Kevlar® and Teijin Twaron's Twaron® are aramid fibers.
Believe it or not, HPPE fibers are made of the same basic materials that go into plastic milk cartons--but with a different structure--and they are capable of very good ballistic performance. Due to the chemical structure of these HPPE fibers, they are actually more like a plastic than a fiber, thus movement of air and release of moisture through the fabric is much more difficult. Many armor manufacturers have worked diligently to engineer solutions to these two problems.
Aramid fibers were developed in the mid-1960s by DuPont. Aramids are a subgroup of polyamides (nylon). However, due to differences in their molecular structure, they are capable of much greater ballistic performance. These are multifilament synthetic fibers characterized by very low flammability and no melting point, as well as very good fabric integrity at higher temperatures. Aramids contain aromatic rings--chemical structures that are very strong. These rings are combined into long molecules that are very linear in nature. These structures have to have some "give", but not too much. A good analogy is a glass window as opposed to a Plexiglas window: glass is brittle, a bee that flies into it will bounce off, but a baseball will shatter it. Plexiglas, on the other hand, has some give. A baseball will bounce off, but a bullet will penetrate it. The degree to which the window is resistant to a force hitting it is a function of the mass and velocity of the object combined with the flexible structure of the window.
By the way--consider this: when a bullet strikes a piece of bullet resistant material, that material has to instantly slow the projectile from a speed of perhaps 1,400 feet per second to zero feet per second. That is a tremendous amount of energy--where does it go? The law of conservation of energy tells us that it has to go somewhere--it doesn't just disappear. It travels outwards, along the strands of bullet resistant fiber, dissipating as it goes, while some is conveyed through the ballistic panel (although the projectile is stopped, some of the energy continues forward as it diminishes). The challenge for body armor fiber manufacturers, fabric weavers, and armor manufacturers, is to develop products that will dissipate the energy in the proper ratio, so that the projectile will stop and the energy will dissipate with minimal injury to the wearer.