  Interpretability logics are endowed with relational semantics \`a la Kripke:
Veltman semantics. For certain applications though, this semantics is not
fine-grained enough. Back in 1992, in the research group of de Jongh, the
notion of generalised Veltman semantics emerged to obtain certain
non-derivability results as was first presented by Verbrugge ([76]). It has
turned out that this semantics has various good properties. In particular, in
many cases completeness proofs become simpler and the richer semantics will
allow for filtration arguments as opposed to regular Veltman semantics. This
paper aims to give an overview of results and applications of Generalised
Veltman semantics up to the current date.
