We review a class of 3D lattice spin models in which planar Peierls boundaries between + and - spins can be created at zero energy cost. These so-called Gonihedric Ising models have (in general) specially tuned nearest neighbour, next-to-nearest neighbour and plaquette interactions, which endow the models with some novel properties both in and out of equilibrium. After reviewing the genesis of the models in string theory, we discuss investigations of both their equilibrium and non-equilibrium behaviours by various analytical and numerical means. The purely plaquette variant of the model displays all the standard indications of glassy behaviour without any recourse to quenched disorder, whilst still possessing a crystalline low-temperature phase in equilibrium. © 2008 Springer-Verlag Berlin Heidelberg.