## 1 Introduction  
Within the last 15 years, materials and structures showing geometric dimensions below 100 nm have gained more and more attraction to the scientific world and stimulated spirit of research on sometimes fancy ideas for future applications like molecular manufacturing or space elevators as well as on serious products for consumer goods, health, medical or food technology [1-5]. With respect to the almost infinite numbers of scientific reports, books, and journal contributions on nanoscience and nanotechnology, the authors of this review article concentrate on some elementary considerations on inorganic nanoparticle properties, basic remarks on synthesis and processing challenges, functional properties and applications of polymer-nanoparticle-composites, as well as on modern research fields, where these polymer matrix composites play a decisive role:  
* optical and magnetic properties
* microelectronic devices
* piezoelectric actuators and sensors
* electrolytes, anodes in lithium-ion-batteries and supercapacitors
* organic solar cells and intrinsic conductive polymers
* photoresists used in microelectronics and microsystems technologies
* biomedical sciences. Before discussing various synthesis methods and properties of nanocomposites, one has to consider elementary consequences of the small size of nanoparticles. Nanoparticles are, by definition, particles with diameters below the micron dimension: generally, below 0.1 um (100 nm). A more stringent definition considers nanoparticles as particles with properties depending directly on their size. Examples are optical, electrical, or magnetic properties. Therefore, in many cases the latter definition restricts nanoparticles to particles with sizes below 10-20 nm. Additionally, with decreasing particle size, the ratio of surface/volume increases, so that surface properties become crucial. The dependency of surface/volume ratio is a function of size. In this context, it is important to realize that e.g., 5 nm particles consist of only a few 1000 atoms or unit cells and possess approximately 40% of their atoms at the surface. In contrast, 0.1 um particles contain some \(10^{7}\) atoms or unit cells, and only 1% of their atoms are located at the surface. Therefore, the smaller the particles are, the more important will be surface properties, influencing interfacial properties, agglomeration behavior, and also - as will be shown later - physical properties of the particles. As the surface area of nanoparticles is some 100 m\({}^{2}\)/g, contaminations stemming from the various synthesis processes, as e.g., remaining precursor residuals, or solvents, may additionally influence the surface properties. A very demonstrative example of the influence of surface area, adapted from [6], is to visualize a 50 kg piece of quartz (SiO\({}_{2}\)) in the form of a cube. This cube has a total edge length of about 27 cm. As a single crystal, this piece of quartz would have a total surface area of about 0.44 m\({}^{2}\). Reducing the edge length of the contributing cubes (corresponding to crystal size) to 1 mm, the quartz cube would consist of approximately \(2\times 10^{7}\) small cubes with a total surface area of approximately 120 m\({}^{2}\). A further reduction to 5 nm would lead to approximately \(1.6\times 10^{23}\) very small cubes with a total surface area of around 2 km\({}^{2}\). This is shown schematically in Figure 1.  
Such extremely small particles possess only poor \"compacting properties\". The powder density is very low, so that 100 mg of a nanopowder may take a volume of around 1 cm\({}^{3}\). In the ideal case, assuming monomodal spherical nanoparticles, no friction between the particles, no van-der-Waals forces between the particles, no agglomeration, and a cubic face centered arrangement of particles; a maximum filling degree of 74 vol % can be obtained for a composite. In reality, the filling degree will always be significantly lower.