The increasing integrated luminosity of the data collected at the major Large Hadron Collider experiments - ALICE, ATLAS, CMS and LHCb - necessitates increasingly large simulated samples. Given that the computational resources won't grow proportionally to the integrated luminosity, how can the experiments produce these large samples? A key technique the experiments use to address this challenge is replacing traditional detector simulation with generative machine learning models. These generative models achieve O(10-1000) times improvements in computational efficiency while maintaining high accuracy. Specifically, I discuss four solutions: ALICE's simulation of Zero Degree Calorimeter with a Variational Autoencoder, ATLAS's use of Generative Adversarial Networks for calorimeter simulation, CMS's end-to-end FlashSim simulation based on Normalising Flows, and LHCb's Lamarr pipe-line employing Generative Adversarial Networks. The speed-up and physics performance achieved by these solutions cements the status of generative models as a viable, faster alternative to the established simulation techniques, which is an important step towards addressing the computational demands of the current and future LHC data analyses.