They have a wide variety of uses. Big ones include some varieties of batteries, magnets (NdFeB, SmCo), phosphors, doped fiber optical amplifiers (very important for global fiber optic networks), Nd-YAG lasers, catalysts for oil processing, contrast agents for MRI (gadolinium). There's even a drug for osteoporosis containing lanthanum.

Some rare earths have extraordinarily high thermal neutron capture cross sections, in the millions of barns. Gadolinium is used as a "burnable absorber" in some nuclear reactors, particularly naval reactors: as the fuel is consumed, the absorber also burns down, reducing the reactivity change.