Hybrid materials, or hybrids incorporating both organic and inorganic constituents, are emerging as a very potent and promising class of materials due to the diverse, but complementary nature of the properties inherent of these different classes of materials. The complementarity leads to a perfect synergy of properties of desired material and eventually an end-product. The diversity of resultant properties and materials used in the construction of hybrids, leads to a very broad range of application areas generated by engaging very different research communities. We provide here a general classification of hybrid materials, wherein organics–in-inorganics (inorganic materials modified by organic moieties) are distinguished from inorganics–in–organics (organic materials or matrices modified by inorganic constituents). In the former area, the surface functionalization of colloids is distinguished as a stand-alone sub-area. The latter area—functionalization of organic materials by inorganic additives—is the focus of the current review. Inorganic constituents, often in the form of small particles or structures, are made of minerals, clays, semiconductors, metals, carbons, and ceramics. They are shown to be incorporated into organic matrices, which can be distinguished as two classes: chemical and biological. Chemical organic matrices include coatings, vehicles and capsules assembled into: hydrogels, layer-by-layer assembly, polymer brushes, block co-polymers and other assemblies. Biological organic matrices encompass bio-molecules (lipids, polysaccharides, proteins and enzymes, and nucleic acids) as well as higher level organisms: cells, bacteria, and microorganisms. In addition to providing details of the above classification and analysis of the composition of hybrids, we also highlight some antagonistic yin-&-yang properties of organic and inorganic materials, review applications and provide an outlook to emerging trends.