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Magnetization processes in particulate L10 FePt nanostructures are investigated by model calculations and numerical simulations. The systems considered include anisotropic nanograins embedded in non-magnetic matrix; randomly oriented nanoclusters embedded in a C matrix, and nanocomposites of FePt particles in a semi-hard matrix. The reversal mechanisms depend on both intra- and intergranular features. Quasi-coherent rotation dominates the reversal in weakly-coupled granular magnets, but interface imperfections yield a disproportionately strong coercivity reduction. Strong intergranular exchange leads to a transition to a discrete pinning regime, which is accompanied by a coercivity maximum.