Moduli spaces for global G-shtukas appear as function fields analogs for Shimura varieties. This can be observed for example through Langlands philosophy. They possess local counterparts which are called Rapoport-Zink spaces for local P-shtukas which similarly arise as function fields analogs for Rapoport-Zink spaces for p-divisible groups. In this talk we first recall the construction of these moduli stacks (spaces), and after providing some preliminary backgrounds, we discuss the theory of local models for them. If time permits we also discuss some of the applications. 

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