  Trianguline representations are a certain class of p-adic representations of
Gal(Qp^alg/Qp) like the crystalline, semistable and de Rham representations of
Fontaine. Their definition involves the theory of (phi,Gamma)-modules. In this
survey, we explain the theory of (phi,Gamma)-modules and the definition and
properties of trianguline representations. After that, we give some examples of
their occurrence in arithmetic geometry.
