Since the discovery of practical superconductors in the late 1950s/early 1960s, High-Energy Physics (HEP) and fusion have become the drivers of applied superconductivity, and vice versa, superconductivity has enabled the development of ever bigger machines relying on ever higher magnetic fields. After a brief history of the main breakthroughs which have made the Large Hadron Collider (LHC) and the International Thermonuclear Experimental Reactor (ITER) possible, we present a state of art of Low-Temperature and High-Temperature Superconductors (LTS and HTS), and we discuss the prospects and challenges of the next generation of projects that are emerging in both fields.