Appears in collection : Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday

Donagi and Pantev set out a program for the construction of the parabolic logarithmic Higgs sheaves associated to Hecke eigensheaves in the geometric Langlands correspondence. One of the main features is that their spectral varieties over Bun_G are Hitchin fibers viewed birationally as subvarieties of T^*(Bun_G). We'll discuss various aspects of this construction: cases where it is known, the difficulties that can arise, and relationships with the geometry of the Hitchin moduli space.