In this chapter, we describe a model of random planar maps weighted by self-dual Fortuin-Kasteleyn (FK) percolation. This can be thought of as a canonical discretisation of Liouville quantum gravity. We start with some generalities about planar maps and then introduce the FK random map model, which depends on a parameter $q\ge 0$, before explaining the conjectured connection to Liouville quantum gravity. A fundamental tool for studying such random planar maps is Sheffield’s (hamburger-cheeseburger) bijection. We first explain it carefully for tree-decorated maps (the special case of the FK model of planar maps with $q=0$), which correspond under this bijection to random walk excursions in the quarter-plane. We then explain its generalisation to $q\ge 0$ in detail. This is first used to show that the maps possess an infinite volume limit in the local topology. Then, a theorem of Sheffield gives a scaling limit result for these maps. One consequence is that a phase transition takes place at $q=4$. Furthermore, it allows one to compute some associated critical exponents when $q<4$ (which are consistent with the KPZ relation of Chapter 3). These arguments are a discrete analogue of the “mating of trees” perspective on Liouville quantum gravity described in Chapter 9.