The article overviews experimental results obtained by applying Internal PhotoEmission (IPE) spectroscopy methods to characterize electron states in single-or few-monolayer twodimensional (2D) materals and at their interfaces. Several conducting (graphene) and semiconducting (transitional metal dichalcogenides MoS2, WS2, MoSe2, and WSe2) films have been analyzed by IPE, which reveals significant sensitivity of interface band offsets and barriers to the details of the material and interface fabrication indicating violation of the Schottky-Mott rule. This variability is associated with charges and dipoles formed at the interfaces with van der Waals bonding as opposed to the chemically bonded interfaces of three-dimensional semiconductors and metals. Chemical modification of the underlying SiO2 surface is shown to be a significant factor, affecting interface barriers due to violation of the interface electroneutrality.