In uniformly hyperbolic dynamical systems, the Markov structure enables us to learn a lot about the statistical properties: for example the existence of equilibrium states and related thermodynamic properties, the return time statistics, decay of correlations, and so on. In non-uniformly hyperbolic systems - here we focus on interval maps - we can find a related Markov extension, developed by Hofbauer and Keller, which captures all of the dynamics of the original system and allows us to use ideas from the uniformly hyperbolic setting. I will explain how to do this, how it is related to another kind of Markov extension, often called Young towers, and try to give an idea of the kind of results we are then able to prove.