  Atomically-thin magnetic crystals have been recently isolated experimentally,
greatly expanding the family of two-dimensional materials. In this Article we
present an extensive comparative analysis of the electronic and magnetic
properties of ${\rm Cr}_2{\rm Ge}_2{\rm Te}_6$, based on density functional
theory (DFT). We first show that the often-used ${\rm DFT}+U$ approaches fail
in predicting the ground-state properties of this material in both its
monolayer and bilayer forms, and even more spectacularly in its bulk form. In
the latter case, the fundamental gap {\it decreases} by increasing the
Hubbard-$U$ parameter, eventually leading to a metallic ground state for
physically relevant values of $U$, in stark contrast with experimental data. On
the contrary, the use of hybrid functionals, which naturally take into account
nonlocal exchange interactions between all orbitals, yields good account of the
available ARPES experimental data. We then calculate all the relevant exchange
couplings (and the magneto-crystalline anisotropy energy) for monolayer,
bilayer, and bulk ${\rm Cr}_2{\rm Ge}_2{\rm Te}_6$ with a hybrid functional,
with super-cells containing up to $270$ atoms, commenting on existing
calculations with much smaller super-cell sizes. In the case of bilayer ${\rm
Cr}_2{\rm Ge}_2{\rm Te}_6$, we show that two distinct intra-layer
second-neighbor exchange couplings emerge, a result which, to the best of our
knowledge, has not been noticed in the literature.
