The p-adic Langlands programme is a relatively new area in number theory with close connections to modularity results, p-adic geometry, and representation theory. One of the new features compared to the classical theory is that it does not suffice to understand irreducible objects on the automorphic- and the Galois sides as the representations can be very far from being semisimple. Especially, mod p and p- adic principal series representations of GLn(Qp) have many interesting successive extensions and one should connect these to certain extensions of objects on the Galois side. In my talk I first give some overview of the status of the (relevant parts of the) p-adic Langlands programme. Then I define a functor from smooth mod p^n representations of GLn(Qp) to representations of the direct product of n − 1 copies of the absolute Galois group of Qp and one copy of the multiplicative group. This functor is fully faithful when restricted to extensions of principal series. Finally, I formulate a conjecture about what the essential image of this functor should be and provide some evidence for it. The latter is in part joint work in progress with G. Jakovác.