Explore the fascinating world of particle accelerators in this 55-minute lecture by Suzie Sheehy at The Royal Institution. Discover how these powerful machines work, from cyclotrons and synchrotrons to radio frequency and focusing techniques. Learn about the challenges in particle acceleration and the reasons behind ongoing research in this field. Delve into next-generation accelerators, including the intensity frontier and accelerator-driven subcritical systems. Examine the importance of reliability and key parameters in accelerator design. Investigate fixed field alternating gradient accelerators, strong focusing, and oscillations in electron models. Gain insights into Coulomb force, innovative solutions, and the historical context of accelerator development, including JJ Thompson's contributions.