Kevlar is an aramid fiber that is used in ballistics protection vests. From the structure (structure shown from Wikipedia article), you can see why it would work to dissipate the energy from a bullet since there is an extensive network of interactions between the linear chains. The wearer ends up bruised from the force, but unpunctured and avoids serious injury from handguns bullets.
More modern ballistics protection devices use ceramic plates (along with Kevlar) to give greater stab resistance and protection from higher velocity rifle rounds. My question is, what ceramics do they use? Do they have a "flexible" ceramic that will deform to absorb the energy and not break? Or do the plates work by breaking to absorb the energy and, thus, have to be replaced after each event?