  In this article we first survey the analogy between Shimura varieties (resp.
Rapoport-Zink spaces) and moduli stacks for global G-shtukas (resp. Rapooprt
Zink spaces for local P-shtukas). This part is intended to enrich the
dictionary between the arithmetic of number fields and function fields a bit
further. Furthermore, to complete this picture, we also study some local
properties of Rapoport-Zink spaces for local P-shtukas by constructing local
models for them. This provides a "local" complementary to a previous work of
the author, which was devoted to the study of the local models for the moduli
stacks of global G-shtukas. We also discuss some of its applications.
