An important development in the study of multiple zeta values was the realization that the subalgebra of the reals they generate is the homomorphic image of a subalgebra of QSym, the algebra of quasisymmetric functions. Now QSym admits a Hopf algebra structure, and this has provided some insights into the multiple zeta values. We will bring this picture up date by discussing Hopf algebra structures on more general quasi-shuffle algebras and their applications.