  This thesis deals with a class of integrable field theories called models
with twist function. The main examples of such models are integrable non-linear
sigma models, such as the Principal Chiral Model, and their deformations. A
first obtained result is the proof that the so-called Bi-Yang-Baxter model,
which is a two-parameter deformation of the Principal Chiral Model, is also a
model with twist function. It is then shown that inhomogeneous Yang-Baxter type
deformations modify certain global symmetries of the undeformed model into
Poisson-Lie symmetries. Another chapter concerns the construction of an
infinite number of local charges in involution for all integrable sigma models
and their deformations : this result is based on the general formalism shared
by all these models as field theories with twist function.
  The second part of the thesis concerns Gaudin models. These are integrable
models associated with Lie algebras. In particular, field theories with twist
function are related to Gaudin models associated with affine Lie algebras. A
standard approach for studying the spectrum of quantum Gaudin models over
finite algebras is the one of Feigin-Frenkel-Reshetikhin. In this thesis,
generalisations of this approach are conjectured, motivated and tested. One of
them deals with the so-called cyclotomic finite Gaudin models. The second one
concerns the Gaudin models associated with affine Lie algebras.
