Liquid crystal polymer composite systems can be divided into two main subgroups. The first consists of the polymer dispersed liquid crystals (PDLC), where the liquid crystal is dispersed in the continuous polymer matrix. The second contains the liquid crystal dispersed polymer (LCDP) systems (sometimes called as liquid crystal/gel dispersions), where only a small amount of polymer is dispersed in a continuous liquid crystal matrix. Neutron scattering and optical studies on various LCDP systems were made to investigate the structure of polymers dispersed in nematic and smectic liquid crystals. The results indicate that small (<100 Angstrom size) fuzzes on the surface of the polymer fibers may play the essential role in the alignment of the liquid crystal molecules. These fuzzes can be realigned by the combination of external fields and heat treatments yielding a fading memory effect. This implies various application possibilities. Among them we describe a novel, electrically driven optical storage effect.