Ceramics in "bullet proof" vests?
As far as I can tell there are two material types used for this - pure ceramics or ceramic mixtures that are designed to break and be replaced, and composite metal + ceramic materials that are designed to be able to handle a couple of rounds without losing too much effectiveness. There are also techniques involving purely metal layers in overlapping structures with fibers of materials like Kevlar or ultra-high-molecular-weight polyethene (UHMWPE) (of which Spectra is a brand).

Shopping around, it seems the best materials are boron and silicon carbides (extremely hard materials, though not quite as hard as diamond), which can be formed into plates with multiple levels of structure by starting with hexagonal plates and forming larger plates from those. In addition to personal armour, the same materials and techniques are used for military vehicle (including aircraft) armour. In the ceramic/metal composite materials, you get ceramic plates formed up within a metal sheet, where a ceramic element will shatter to take most of the impact, while the rest will be absorbed by the metal matrix. The metal matrix then remains intact (but may be deformed) so that the armour is still useful but weakened around the area of impact.

Good places to start from are the Wikipedia pages for Chobham armour (the common name for the tank armour that includes composite metal/ceramic matrix materials), and Small Arms Protective Insert.