In seminal paper, Gessel-Reutenauer construct a truly remarkable bijection between words in the free monoid over an infinite alphabet and multisets of primitive necklaces. Using this bijection Gessel-Reutenauer derive a variety of beautiful symmetric function identities with deep implications in permutation enumeration. In this talk we review the Gessel-Reutenauer results, derive some applications and state some challenging combinatorial problems.