  We analyze magnetic properties of monolayers and bilayers of chromium
trihalides, CrI$_3$, in two different stacking configurations: AA and
rhombohedral ones. Our main focus is on the corresponding Curie temperatures,
hysteresis curves, equilibrium spin structures, and spin wave excitations. To
obtain all these magnetic characteristic, we employ the atomistic spin dynamics
and Monte Carlo simulation techniques. The model Hamiltonian includes isotropic
exchange coupling, magnetic anisotropy, and Dzyaloshinskii-Moriya interaction.
Though the latter is relatively weak in CrI$_3$, we consider a more general
case assuming also an enhancement of Dzyaloshinskii-Moriya interaction in the
corresponding Janus structures and by external electric fields. An important
issue of the analysis is the correlation between hysteresis curves and spin
configurations in the system, as well as formation of the skyrmion textures.
