  We give an expository account of the theory of intertwining operators for
connected reductive $p$--adic groups, and their connection with automorphic
$L$--functions. Our purpose is to illustrate the relation between harmonic
analysis and arithmetic. In particular, we describe how the theory of
Plancherel measures allows us to compute certain local Langlands
$L$--functions. In order to be more self contained, we give a brief
introduction to the Langlands program. The theory of $R$--groups and elliptic
representations is treated here as well. Finally, we give an example which
illustrates how the theory of twisted endoscopy plays a crucial role in
determining the poles of both the intertwining operators and the local
Langlands $L$--functions in question. A version of this manuscript, in revised
form, will appear as a chapter in the proceedings of the conference ``Teoria de
Representaciones de Groupos Algebraicos Sobre Cuerpos Locales y Applicationes''
(C. Bushnell, P. Kutzko, J. Pantoja, J. Soto Andrade eds.).
