Why should we care about rare earth metals?

For decades now, China has had a stranglehold on the production of rare earth metals, and it is far from clear how the rest of the world is going to ever break that stranglehold. But as we have seen repeatedly, over-reliance on China is always a bad idea, and breaking that stranglehold is probably in everyone's (but China's) interests.
Rare earth metals or elements are a group of 17 broadly similar metals that have unique properties making them uniquely useful for a range of commercial purposes, particularly in the technology sector, and even more particularly in military and "clean" technologies. Mobile phones, wind turbines, electric cars, light bulbs, solar panels, high-temperature magnets, lasers, fibre optics, MRI machines, and military drones all use them to some extent. They are used for polishing optical-quality glass, for air pollution control, for illuminated screens on electronic devices, and many other essential 21st century uses.
Most of the names may not mean much to you: cerium, dysprusium, erbium, europium, gadolinium, holmium, lanthanum, lutetium, neodymium, praseodymium, promethium, samarium, scandium, terbium, thulium, ytterbium, and yttrium. Although not actually rare in the global scheme of things, it is rare to find them in economically-extractable quantities, and they are produced in vanishingly small amounts compared to more mainstream mining products like copper or zinc.
Up until the 1980s, the USA was the main producer, but in the 1990s Chinese production surged, and today China produces around 80% of the world's output, mainly in the Inner Mongolia region, followed by the USA and Australia. China also has by far the greatest reserves, followed by Brazil, Vietnam, Russia, India, Australia and Greenland (see why Donald Trump wanted to buy Greenland now?)
In order to compete against China on the uneven playing field they have built up over the years, Western countries are going to have to beat China at their own game, with government intervention and capital commitment on a large scale to beef up their industries in order to compete. Chinese rare earth companies, with state help, can produce at prices low enough to drive most competitors out of business.
Companies (and consumers) that use rare earth metals may also have to suck it up and pay more for their supplies, or possibly even accept compromises on the environmental front, which would be an unfortunate development. A substantial proportion of China's production comes from small, rural and illegal opertions with little or no environmental regulation, and even its main official production in Inner Mongolia has led to major environmental damage and degradation. By its very nature, rare earth mining produces a lot of toxic and radioactive wastewater and tailings, which can leach acids, heavy metals and radioactive elemwnts into the groundwater.
Another avenue to explore is the recycling of rare earths from existing products, an area that Japan in particular is pursuing. There are challenges, but as prices of rare earths rise, recycling is becoming an increasingly economical option.