Collider physics, with the LHC as a key player, is one of the most important fields of Particle Physics. I will start my presentation with a brief description of how collider experiments study fundamental interactions. \par I will then show that, by looking at rare phenomena, one naturally ends up in a situation where multiple proton-proton collisions happen simultaneously. This effect, where a potentially interesting collision is contaminated by the presence of the other simultaneous collisions is called pileup. To achieve the best possible measurements, and hence maximise our learning potential, one should correct for pileup contamination. This is the subject of this habilitation thesis. \par After a generic introduction, I will describe the area--median method that has been extensively used at the LHC so far. I will then present several ideas trying to reach a better resolution. A special emphasis will be put on analytic arguments and understanding of pileup mitigation. I will conclude with a discussion of open questions and future prospects.