50th anniversary of the Judd-Ofelt theory: An experimentalist's view of the formalism and its application

► We review the theory of 4f transition intensities developed by Judd and Ofelt. ► We present the formalism for calculating 4f wavefunctions. ► We discuss the Judd-Ofelt theory and its practical applications. ► The theory is illustrated on the example of LaCl3:Er.