 In 2006, Jonathan Pila and Alex Wilkie showed that provided one removes the subsets defined using only polynomial inequalities, subsets of Rn definable in an o-minimal expansion of the real field have few rational points. Subsequently, following a strategy first employed by Pila and Umberto Zannier to reprove the Manin-Mumford conjecture various authors have used this o-minimal counting theorem to solve some important open problems in diophantine geometry. 