Abramovich and Vistoli introduced the notion of a twisted curve in order to define compact moduli spaces of stable maps into a Deligne--Mumford stack. In this talk I will discuss an equivalence between this notion of twisted curve and a new notion of log twisted curve, which is a nodal curve equipped with some logarithmic data (in the sense of Fontaine and Illusie). Then I will discuss various applications of this equivalence, and in particular explain how it can be combined with a general theory of Hom--stacks to give simple proofs of the existence and boundedness of the moduli of twisted stable maps into a Deligne--Mumford stack.