  In this brief review we introduce the Landau-Ginzburg/conformal field theory
correspondence, a result from the physics literature of the late 80s and early
90s which predicts a relation between categories of matrix factorizations and
categories of representations of vertex operator algebras. To date there is no
precise mathematical statement for it. Here, we explain some recent examples of
this correspondence, some standing conjectures and future directions of
research.
