Monte Carlo event generators are among the most used tools in high-energy physics today. As an introduction, I will explain what is their role in modern collider phenomenology. The talk will focus on a central part of Monte Carlo generators, the parton shower, which essentially covers all the scales between the hard scale of the collision and the non-perturbative scale. I will describe how typical parton-shower algorithms are built. I will then report on a recent work (arXiv:2020:11114) where we introduced a new set of parton showers aimed at achieving an unprecedented (logarithmic) accuracy.