Rare earth metals actually are not rare, they are simply more expensive to mine than most metals. The rare earth elements are contained in iron ore tailings in the mid-west US among other places.  China controls much of the market. China produces around 87% of rare earth metals now, their less stringent environmental regulations mean the refining process is less expensive than in the US.
They are critical to high-performance optics and lasers, and essential to the most powerful magnets and superconductors in the world.  They are useful for the defense industry.  Rare earth metals are good for use in high-tech applications.  Rare earth metals are not as profitable as some other ore,  This has made them less desirable in the past thus giving the name rare earth. 
Rare earth elements are millimeter-sized crystals known as fluorapatite found in deposits of iron ore.  When the iron was mined, the fluorapatite was usually left behind as waste since it was considered an unwanted impurity.  
The ores are rich in yttrium, lanthanum, and neodymium.  Chinese dominance of rare earth supplies causes problems as China restricts export, it imposed quotas on the metals.  The market research study provides insight into market driving forces, assessment of market opportunities, market share analysis, and market forecasts.