  This is a report on results and methods in the reduction modulo p of Shimura
varieties with parahoric level structure. In the first part, the local theory,
we explain the concepts of parahoric subgroups, of the mu-admissible and
mu-permissible subsets of the Iwahori-Weyl group, of the corresponding union of
affine Deligne-Lusztig varieties and of local models. In the second part, the
global theory, we use these concepts to formulate conjectures on the points in
the reduction modulo p of Shimura varieties with parahoric level structure.
