p-adic L-functions for GL(n)

After a general introduction to the idea of p-adic L-functions, I will report on the results obtained in a joint work with Mladen Dimitrov and Fabian Januszewski, in which we construct p-adic L-functions attached to a cohomological cuspidal representation of GL(2n) over a totally real field which admits a Shalika model. The methods we use involve (i) my own previous work with Harald Grobner on the special values of the standard L-function attached to such an object, (ii) a generalization of Dimitrov's automorphic symbols, and (iii) analogues of Januszewski's work on p-adic L-functions in some other automorphic contexts.