It has been for a long time recognized that nanoparticles are of great scientific interest as they are effectively a bridge between bulk materials and atomic structures. At first, size effects occurring in single elements have been studied. More recently, progress in chemical and physical synthesis routes permitted the preparation of more complex structures. Such structures take advantages of new adjustable parameters including stoichiometry, chemical ordering, shape and segregation opening new fields with tailored materials for biology, mechanics, optics magnetism, chemistry catalysis, solar cells and microelectronics. Among them, core/shell structures are a particular class of nanoparticles made with an inorganic core and one or several inorganic shell layer(s). In earlier work, the shell was merely used as a protective coating for the core. More recently, it has been shown that it is possible to tune the physical properties in a larger range than that of each material taken separately. The goal of the present review is to discuss the basic properties of the different types of core/shell nanoparticles including a large variety of heterostructures. We restrict ourselves on all inorganic (on inorganic/inorganic) core/shell structures. In the light of recent developments, the applications of inorganic core/shell particles are found in many fields including biology, chemistry, physics and engineering. In addition to a representative overview of the properties, general concepts based on solid state physics are considered for material selection and for identifying criteria linking the core/shell structure and its resulting properties. Chemical and physical routes for the synthesis and specific methods for the study of core/shell nanoparticle are briefly discussed.