The transition to a low-carbon economy is accelerating also thanks to the 2016 Paris Agreement and the Sustainable Development Goals, adopted by the United Nations General Assembly in 2015. The conditions are therefore in place for reducing by 2050 the production of energy using coal or natural gas to a minimum or to zero. Unfortunately, however, the new “clean” or “green” energy technologies depend very much on the availability and cost of certain elements called rare earths. The availability of some of these materials is at risk due to their inaccessibility, their vulnerability to supply interruptions and the lack of suitable substitutes. This work briefly examines the industrial demand for these elements, some of their applications and the geological and geopolitical difficulties for their supply.