This paper is a short review of recent results on interface states in the
Falicov-Kimball model and the ferromagnetic XXZ Heisenberg model. More
specifically, we discuss the following topics: 1) The existence of interfaces
in quantum lattice models that can be considered as perturbations of classical
models. 2) The rigidity of the 111 interface in the three-dimensional
Falicov-Kimball model at sufficiently low temperatures. 3) The low-lying
excitations and the scaling of the gap in the 111 interface ground state in the
ferromagnetic XXZ Heisenberg model in three dimensions. 4) The existence of
droplet states in the XXZ chain and their properties.