  We compare GGA+U calculations with available experimental data and analyze
the origin of magnetic anisotropies in MnF$_2$, FeF$_2$, CoF$_2$, and NiF$_2$.
We confirm that the magnetic anisotropy of MnF$_2$ stems almost completely from
the dipolar interaction, while magnetocrystalline anisotropy energy plays a
dominant role in the other three compounds, and discuss how it depends on the
details of band structure. The latter is critically compared to available
optical measurements. The case of CoF$_2$, where magnetocrystalline anisotropy
energy strongly depends on $U$, is put into contrast with FeF$_2$ where
theoretical predictions of magnetic anisotropies are nearly quantitative.
