The nanocomposites described here all involve polymers and were chosen because they are already of commercial importance, show some promise of becoming so, or simply seem interesting. The field is so broad that some topics are mentioned only very briefly, and there is considerable emphasis on the polysiloxane nanocomposites studied by the author's research group. Some are typically prepared using techniques very similar to those used in the new sol-gel approach to ceramics, with either the polymer or the ceramic being the continuous phase. Other dispersed phases include particles responsive to an applied magnetic field, intercalated or exfoliated platelets obtained from clays, mica, or graphite, silsesquioxane nanocages, nanotubes, dual fillers, porous particles, spherical and ellipsoidal polymeric particles, and nanocatalysts. Also described are some typical studies involving theory or simulations on such particle reinforcement. Experiments on ceramics modified by dispersed polymers are equally interesting, but there is less relevant theory. Many of the fields mentioned have become so vast that the approach taken here is simply to describe general approaches and characteristics of the composites, list some specific examples, and provide leading references (with some emphasis on studies that are relatively recent or in the nature of reviews).