  In this colloquium, we review the research on excitons in van der Waals
heterostructures from the point of view of variational calculations. We first
make a presentation of the current and past literature, followed by a
discussion on the connections between experimental and theoretical results. In
particular, we focus our review of the literature on the absorption spectrum
and polarizability, as well as the Stark shift and the dissociation rate.
Afterwards, we begin the discussion of the use of variational methods in the
study of excitons. We initially model the electron-hole interaction as a
soft-Coulomb potential, which can be used to describe interlayer excitons.
Using an \emph{ansatz}, based on the solution for the two-dimensional quantum
harmonic oscillator, we study the Rytova-Keldysh potential, which is
appropriate to describe intralayer excitons in two-dimensional (2D) materials.
These variational energies are then recalculated with a different
\emph{ansatz}, based on the exact wavefunction of the 2D hydrogen atom, and the
obtained energy curves are compared. Afterwards, we discuss the Wannier-Mott
exciton model, reviewing it briefly before focusing on an application of this
model to obtain both the exciton absorption spectrum and the binding energies
for certain values of the physical parameters of the materials. Finally, we
briefly discuss an approximation of the electron-hole interaction in interlayer
excitons as an harmonic potential and the comparison of the obtained results
with the existing values from both first--principles calculations and
experimental measurements.
