Critical materials represent mostly metals having a big importance for the future of the economy in the European countries. It is very difficult to replace these critical metals by other metals. Because of their wide application, the demand for these metals is increased, but the production cannot follow their growing consumption. Rare earth elements (REE) belong to critical materials. They include 17 elements, very similar in terms of their chemical and physical properties due to their mineralogical structure (the best-known are lanthanum and thorium, which is radioactive). REE are divided into elements with a lower atomic mass and elements with a higher atomic mass. Heavier metals show a significantly lower presence in the upper earth crust. In 2010, the share of the REE production in China in the global production amounted to 97 %, constituting a near-monopoly in the world market. In different studies, the term “Strategic” is often used instead “of “critical” materials. The materials for military application are called “Strategic” (nickel). In comparison to strategic metals, critical materials have a big importance for the national economies of European countries (platinum group of metals, rare earth elements, cobalt). The European Commission prepared a strategic development plan for critical materials in the next twenty years. The rare earth elements The rare earth elements include 15 elements (Z=57 through 71) and Yttrium (Z=39) and scandium. Because of their reactivity and similarity, the REEs were found to be difficult to obtain.. Lanthanide elements with a low atomic number are generally more abundant in the earth crust than those with high atomic numbers. World demand for rare earth elements is estimated by Humphries (CRS Report for Congress) at 134.000 tons per year, with the global production of around 114.000 tons annually. Humphries has reported in 2010 that there is no rare earth mine production in the United States. The major uses for rare earth elements include applications in auto catalysts, petroleum refining, metal alloys, cell phones, portable DVDs, etc. Permanent magnets containing neodymium, gadolinium and dysprosium are used in numerous electrical components and generators for wind turbines. The primary defense application (underwater mine detection, satellite power and communication systems, radar systems,etc.) use new materials: Neodymium Iron Boron, Samarium Cobalt. REEs extraction from monazite is performed by dissolution in a hot concentrated base or acid solutions. After cooling, the hydroxides of REEs and thorium are recovered by filtration, and thorium is separated by dissolution and selective precipitation. Metallurgy of indium Indium belongs to the group of rare earth elements with a low melting point. Some addition of indium increases the strength, hardness and corrosion resistance of alloys. The most known producers are situated in Belgium, Canada, Russia, France and Japan. Indium is used as coating on metals applied in difficult operation conditions, and in semiconductor techniques for the production of diodes. It is formed as a semi-product after pyrometallurgical and hydrometallurgical treatment of sulphidic raw materials. Indium can be used with other valuable metals such as vanadium, thallium, gallium, germanium, and cadmium. The coating process based on Indium is performed by an electrolytic treatment on the surface. Metallurgy of yttrium Yttrium compounds found interesting application in many fields. In particular, yttrium is used in the manufacture of superconductors, in super alloys of nickel and cobalt, and solid oxide fuel cells. Yttrium oxide has a high melting point and is used in ceramics. The compounds of yttrium are also used as catalysts. The growing industrial application of the rare earth elements led to a growing interest in finding new technologies for their recoveries. The selective dissolution of yttrium from lanthanum is performed by ammonium carbonate leaching. Conclusion The EU Raw materials Initiative was decided to identify a list of critical raw materials at the EU level. The EU-report describes a selection of 41 minerals and metals. Then, 14 elements were chosen as critical materials fort the economy of the European countries in the next twenty years. The future use of REEs is expected to be increased in the European countries. About 90 % of metal alloys are produced in China. The price of rare earth elements is reduced for the consumers in China in comparison to some companies in the USA and Europe. Therefore, the European countries and the USA have protested against this situation. The selective winning of rare earth elements is the most important aim in the processing of raw materials. The combination of pyrometallurgical and hydrometallurgical methods might be a new way of solving this problem in the European countries.