This workshop is being run under the auspices of the MAGMA Computer Algebra Group (University of Sydney), and is devoted to computational aspects of the the theory of p-adic L-functions. This topic has a rich history both in itself and in relation to global L-functions. It is only recently that the ability to explore various conjectures has become practical. An explicit example is with p-adic variants of Stark's conjectures, which have been investigated at least in the abelian case. In some contexts, the computations have truly acted as an “experimental science”, in that the final refinements of the conjectures were largely aided by the numerical data. Another development has been the application of overconvergent modular symbols to facilitate the computation of the p-adic L-functions of modular forms, and here the connection with elliptic curves is also of interest. Finally, the well-known cross-germinations with Iwasawa theory will also be highlighted. Our goal is to bring together a targeted group of experts on both the theoretical and computational sides of this subject, so as to share and exposit the latest results, and determine the viable prospects for future work.