The dimensionality of nanosystems plays an important role in nanoscicnce and nanotechnology. In nanostructures with OD macroscopic extension (OD - nanocrystals), 1D macroscopic extension ( I D - nanowires), or 2D macroscopic extensions (2D - nanolayers), novel properties emerge compared to macroscopic bulk systems due to quantum conlincment, charge quantization, magnetic exchange length, etc. In the case of semiconductor systems, the nanostructures of different dimensionality are often called quantum dots, quantum wires, and quantum wells. Dimensionality effects of nanostructures have been introduced with some exemplary features in Chap. 1 and have been shown to be of relevance in synthesis . In the present section some generic characteristics of nanocrystals, nanowires, and nanolayers will be discussed. Dimensionality effects will be resumed later in nanoscale carbon systems and in the discussion of nanomagnetism . Nanodots exhibit in all three spatial directions and dimensions smaller than the dc Broglic wave length of the charge carriers. Semiconductor nanodots are often embedded in another dielectric semiconductor matrix . Single quantum dots may provide innovative components for quantum information processing, quantum cryptography, or hybrid DRAM/Flash data storage. In large numbers (billions) they may form optoelectronic components, lasers or amplifiers, and new systems for communication technology, consumer electronics, or high-precision metrology