  This document is a thesis presented for the ``Habilitation \`a diriger des
recherches''. The first chapter provides some background and sketch the story
of the classical Schur-Weyl duality and its quantum analogue involving the
Hecke algebra. Quantum groups and their centralisers are discussed along with
their connections with the braid group, the Yang-Baxter equation and the
construction of link invariants. A quick review of several related notions of
Hecke algebras concludes the first chapter. The second chapter presents the
fused Hecke algebras and an application to the construction of solutions for
the Yang-Baxter equation. The third chapter summarises recent works on diagonal
centralisers of Lie algebras, and gives an application to the study of the
missing label for sl(3). The last chapter discusses algebraic results on the
Yokonuma-Hecke algebras and their applications to the study of link invariants.
