The large rate of multiple simultaneous proton-proton interactions, or pile-up, generated by the Large Hadron Collider in Run 1 required the development of many new techniques to mitigate the adverse effects of these conditions. This paper describes the methods employed in the ATLAS experiment to correct for the impact of pile-up on jet energy and jet shapes, and for the presence of spurious additional jets, with a primary focus on the large 20.3 [Formula: see text] data sample collected at a centre-of-mass energy of [Formula: see text]. The energy correction techniques that incorporate sophisticated estimates of the average pile-up energy density and tracking information are presented. Jet-to-vertex association techniques are discussed and projections of performance for the future are considered. Lastly, the extension of these techniques to mitigate the effect of pile-up on jet shapes using subtraction and grooming procedures is presented.