  $BF$ gravity comprises all the formulations of gravity that are based on
deformations of $BF$ theory. Such deformations consist of either constraints or
potential terms added to the topological $BF$ action that turn some of the
gauge degrees of freedom into physical ones, particularly giving rise to
general relativity. The $BF$ formulations have provided new and deep insights
into many classical and quantum aspects of the gravitational field, setting the
foundations for the approach to quantum gravity known as spinfoam models. In
this review, we present a self-contained and unified treatment of the $BF$
formulations of $D$-dimensional general relativity and other related models,
focusing on the classical aspects of them and including some new results.
