  The morphology of haloes inform about both cosmological and galaxy formation
models. We use the Minkowski Functionals (MFs) to characterize the actual
morphology of haloes, only partially captured by smooth density profile, going
beyond the spherical or ellipsoidal symmetry. We employ semi-analytical haloes
with NFW and $\alpha\beta\gamma$-profile and spherical or ellipsoidal shape to
obtain a clear interpretation of MFs as function of inner and outer slope,
concentration and sphericity parameters. We use the same models to mimic the
density profile of $N$-body haloes, showing that their MFs clearly differ as
sensitive to internal substructures. This highlights the benefit of MFs at the
halo scales as promising statistics to improve the spatial modeling of dark
matter, crucial for future lensing, Sunyaev-Zel'dovich, and X-ray mass maps as
well as dark matter detection based on high-accuracy data.
