The descent algebra of the symmetric group has played an important role in the understanding of the symmetric group and mathematics in general. One famous example of their applicability is that of Bayer and Diaconis who used a subalgebra of the descent algebra to determine the minimum number of shuffles needed to "randomize" a deck of cards. The descent algebra has also been used towards understanding the representations of the symmetric group. Further, this algebra has close ties to quasi-symmetric function and the peak algebra. The first part of the talk will present a combinatorial introduction to the descent and peak algebras. During the second part of the talk I will discuss recent work with Mathas on a generalization of descent algebras to complex reflection groups. In particular, we have introduced an algebra that follows the construction given by Solomon in terms of "Young" subgroups. This talk will be presented from a combinatorial perspective and it will be self-contained. This talk will be accessible to advanced undergraduates.