  Ferromagnetic van der Waals (vdW) insulators are of great scientific interest
for their promising applications in spintronics. It has been indicated that in
the two materials within this class, CrI$_3$ and VI$_3$, the magnetic ground
state, the band gap, and the Fermi level could be manipulated by varying the
layer thickness, strain or doping. To understand how these factors impact the
properties, a detailed understanding of the electronic structure would be
required. However, the experimental studies of the electronic structure of
these materials are still very sparse. Here, we present the detailed electronic
structure of CrI$_3$ and VI$_3$ measured by angle-resolved photoemission
spectroscopy (ARPES). Our results show a band-gap of the order of 1 eV, sharply
contrasting some theoretical predictions such as Dirac half-metallicity and
metallic phases, indicating that the intra-atomic interaction parameter (U) and
spin-orbit coupling (SOC) were not properly accounted for in the calculations.
We also find significant differences in the electronic properties of these two
materials, in spite of similarities in their crystal structure. In CrI$_3$, the
valence band maximum is dominated by the I 5{\it p}, whereas in VI$_3$ it is
dominated by the V 3{\it d} derived states. Our results represent valuable
input for further improvements in the theoretical modeling of these systems.
