In the first part of this talk we introduce a classical family of symmetric polynomials called Schur polynomials and discuss some of their properties, and a problem that arises from their study, namely the combinatorial interpretation of Littlewood–Richardson coefficients.

In the second part, we explain how the work of Robinson, Schensted, Knuth, Lascoux, and Schuetzenberger on words in an ordered alphabet led to a solution of this combinatorial problem. We will then mention some relatively recent developments in this subject.