  The notions Hodge-Newton decomposition and Hodge-Newton filtration for
F-crystals are due to Katz and generalize Messing's result on the existence of
the local-\'etale filtration for p-divisible groups. Recently, some of Katz's
classical results have been generalized by Kottwitz to the context of
F-crystals with additional structures and by Moonen to $\mu$-ordinary
p-divisible groups. In this paper, we discuss further generalizations to the
situation of crystals in characteristic p and of p-divisible groups with
additional structure by endomorphisms.
